Problem of the Month(July 2013)

In August 2000, we investigated Friedman numbers. In April 2012, we investigated non-integral Friedman numbers, and almost Friedman numbers, both of which have been moved here for organizational purposes. This month we investigate two new related problems.

A fractional Friedman number is a terminating or repeating decimal that can be written in another way using its digits, the four basic arithmetic operations, exponentiation, and parentheses. Notice that a decimal point is required in the number, but not allowed in the expression to make that number. If a number can be written with its digits in order, we call it a nice fractional Friedman number and show it in red. What (nice) fractional Friedman numbers can you find?

A redundant Friedman number can be written with a subset of its digits. Given a set of digits that is not used, what is the smallest redundant Friedman number including those digits that can be written without those digits?

Solvers this month include Bryce Herdt, Jon Palin, Joe DeVincentis, and Hans Havermann.

Here are the known terminating fractional Friedman numbers with 5 or fewer digits. The ones shown in red have the digits in the correct order. The ones smaller than 1 that use fewer than 5 digits can have any small integer added to them.

Known Terminating Fractional Friedman Numbers
 .02125 = 2-5 – 10-2 (JD) .03125 = 0 × 31 + 2-5 (JD) .05125 = 2-5 + 1/50 (JD) .0625 = 260–5 (JD) .06875 = (5 – 7/8) / 60 (JD) .08125 = (1 + 5/8) / 20 (JD) .09375 = 0 + 3 / (9–7)5 (JD) .15625 = 1 / (5×6 + 2) × 5 (JD) .21875 = 21 / 8 / (7+5) (JD) .23125 = (2+3)-1 + 2-5 (JD) .3125 = (3+1)-2 × 5 (JD) .23552 = 23 × (2/5)5 (JD) .24375 = (7 + 4/5) / 32 (JD) .28125 = (2+8–1) / 25 .34375 = (7+4) / (35–3) .3456 = 63 / 54 (JD) .41875 = 1/5 + 7/(4+8) (JD) .43125 = (4-3 + 1/5) × 2 (JD) .4375 = 7 / (5–3)4 .46656 = ((4+6)/6)–5 × 6 (JD) .46875 = (7/8 + 6 – 5) / 4 (JD) .53125 = (5–3)-1 + 2-5 (JD) .54325 = (5/4)-3 + 2-5 (JD) .55296 = (6/5)5 × 2/9 (JD) .59049 = (9/(9+40))5 (JD) .59375 = ((7–9)-5 + 3) / 5 (JD) .625 = 5 / (2+6) .63125 = 3/5 + 21–6 (JD) .6875 = (5–7/8) / 6 (JD) .78125 = (17+8) / 25 .8125 = (1+5/8) / 2 (JD) .84375 = 34 / (8 × (7+5)) (JD) .87501 = 10-5 + 7/8 (JD) .87532 = 7/8 + (3+2)-5 (JD) .9375 = 3 × 5 / (9+7) .96875 = (6 + 7/(9–5)) / 8 (JD) 1.0875 = 7/80 + 15 (JD) 1.1875 = (7 + 1/8) / (1+5) (JD) 1.4592 = 912 / 54 (JD) 1.4625 = 4-2 + (6–1) / 5 (JD) 1.4641 = (1 + 1/(4+6))4 (JD) 1.5625 = 1 × 5 / (6/5 + 2) (JD) 1.75 = 7 / (5–1) 1.875 = -1 / 8 + 7 – 5 (JD) 2.1875 = 2-1 / 8 × 7 × 5 (JD) 2.4125 = (2-4 + 12) / 5 (JD) 2.6125 = 2-4 + 6×2/5 (JD) 2.5 = 5 / 2 2.5584 = (8/5)2 – 5-4 (JD) 2.5875 = (5 + 7/5/8) / 2 (JD) 2.7225 = (2-2 + 7/5)2 (JD) 2.8125 = ((2/8 – 1)2) × 5 (JD) 2.875 = 7 / 2 – 5 /8 (JD) 3.125 = 3 / (1 – 5-2) (JD) 3.1875 = (7 – 5/8) / (3 – 1) (JD) 3.375 = (3/(7–5))3 (JD) 3.4225 = (2 – 3/4/5)2 (JD) 3.5625 = 6 / 5 × (3 – 2-5) (JD) 3.6544 = 4 – 63 / 54 (JD) 3.8416 = ((6+1)/(8–3))4 (JD) 4.125 = 4 × (1 + 2-5) (JD) 4.2125 = (4-2 + 21) / 5 (JD) 4.2375 = 3 / 5 × (7 + 4-2) (JD) 4.4992 = 9 – (9–4)-4) / 2 (JD) 4.5125 = (5 – 1/4)2 / 5 (JD) 4.5927 = 7 × (9/2/5)4 (JD) 4.6875 = (46–8) × 75 (JD) 4.8625 = (8-2 + 6/5) × 4 (JD) 4.875 = (7×5+4) / 8 5.2484 = 42/8 – 5-4 (JD) 5.4432 = 42 × (3/5)4 (JD) 5.625 = 5 / (6 + 2) + 5 (JD) 5.8125 = (5/8 + 1) / 2 + 5 (JD) 6.1875 = 5 + (7+1/8)/6 (JD) 6.875 = 7 – 85–6 (JD) 6.9744 = 7 – (9/6 – 4)-4 (JD) 7.4625 = 4-2 + 7/5 + 6 (JD) 8.5625 = (52 – 5/8) / 6 (JD) 9.5024 = 20 – (9/5)4 (JD) 11.375 = 7 / (1 – 5/13) (JD) 11.875 = -1 × 1 / 8 + 7 + 5 (HH) 12.25 = (1+5/2)2 (JD) 12.875 = 2×(1+5) + 7/8 (JD) 13.125 = 21 / (1 + 3/5) (JD) 13.875 = (1 + 3/8)×5 + 7 (JD) 14.875 = (1 + (4+5)/8) × 7 (JD) 15.384 = 4 × (8/5)3 – 1 (JD) 15.625 = 15/6)-2+5 (JD) 15.975 = 71 / (5 – 5/9) (JD) 16.375 = (6 + 53) / (1+7) (JD) 16.384 = 4 × (8/(6–1))3 (JD) 16.75 = 67 / (5–1) 16.875 = 17 – (6–5)/8 (JD) 18.125 = (21/8 + 1) × 5 (JD) 18.375 = (5/8 + 3 – 1) × 7 (JD) 18.875 = (158 – 7) / 8 (JD) 19.375 = (7/(9–1) + 3) × 5 (JD) 19.75 = 79 / (5–1) (1 + 9/8) × 7 + 5 (JD) 20.875 = 207/8 – 5 (JD) 21.875 = (-21/8 + 7)5 (JD) 23.375 = 35 / 23 – 7 (JD) 24.375 = (7/23 + 4) × 5 (JD) 24.625 = -2-4 × 6 + 25 (JD) 24.875 = 7×4 – 25/8 (JD) 25.125 = 5×5 + 2-2–1 (JD) 25.25 = 5 × 5 + 2-2 (JD) 26.375 = 6×7 – (5/2)3 (JD) 27.375 = 7 – 2-3) × 5 – 7 (JD) 26.875 = (6 – (7–2)/8) × 5 (JD) 28.125 = (5×(1+2))2 / 8 (JD) 28.375 = (7 × 25 + 3) / 8 (JD) 28.875 = (8+25) × 7 / 8 (JD) 29.375 = (7 – 9/23) × 5 (JD) 29.5 = 59 / 2 (JD) 29.875 = 295 / 8 – 7 (JD) 30.375 = 35 / (50+7) 31.875 = -3 – 1 / 8 + 7 × 5 (HH) 32.125 = 25 + 1/23 (JD) 32.375 = (5 – 3/23) × 7 (JD) 32.768 = (8 / (6 – 7/2))3 (JD) 32.875 = (28 + 7) / (3+5) (JD) 33.275 = (7 – 3/2)3 / 5 (JD) 33.875 = 33 / 8 × 7 + 5 (HH) 34.875 = (3–4) / 8 + 7×5 (JD) 35.375 = 3/(5+3) + 7×5 (JD) 35.928 = 9 × (8/2 – 5-3) (JD) 35.992 = (9+9) × 2 – 5-3 (JD) 36.125 = 62 + 1/(3+5) (JD) 36.45 = 36 / 4 / 5 (JD) 36.875 = (–(3–6)/8 + 7) × 5 (JD) 38.375 = 3 / 8 + 3 + 7 × 5 (HH) 38.875 = 3/8 × 85 + 7 (JD) 39.875 = 39 / 8 + 7 × 5 (HH) 40.125 = (2-5 + 10) × 4 (JD) 40.875 = (8 + 7/40) × 5 (JD) 41.875 = 47 – 1/8 – 5 (JD) 42.25 = (4+5/2)2 (JD) 42.875 = 74×2–5 / 8 43.375 = (73 + 4) / (3+5) (JD) 43.875 = 73 / 8 + 5 – 4 (JD) 45.875 = (4+5)×5 + 7/8 (JD) 46.875 = 47 – (6–5)/8 (JD) 47.75 = 7 × 7 – 5 / 4 (JD) 47.875 = 7×7 – (5+4)/8 (JD) 48.125 = 52 – 4 + 1/8 (JD) 48.375 = (7+5)×4 + 3/8 (JD) 48.75 = (7/4+8) × 5 (JD) 49.875 = 4 + 9×5 + 7/8 (JD) 51.875 = 57 – 1/8 – 5 (JD) 53.928 = 9 × (8 – 5-3 + 2) (JD) 54.675 = 67 / 5 / 45 (JD) 56.875 = (5 – 5/8) × (6+7) (JD) 59.375 = 95 / (3 – 7/5) (JD) 59.875 = 9×7 – 5×5/8 (JD) 61.875 = 67 – 1/8 + 5 (JD) 64.125 = (45 + 2) / 16 (JD) 65.875 = 575 / 8 – 6 (JD) 66.875 = 6×(6+5) + 7/8 (JD) 68.125 = 561 / 8 – 2 (JD) 69.875 = 76 – 9/8 – 5 (JD) 71.875 = 77 – 1/8 – 5 (JD) 72.25 = (5+7/2)2 (JD) 72.875 = 527 / 8 + 7 (JD) 76.875 = 77 – (6–5)/8 (JD) 77.875 = 7 × (7 / 8 × 7 + 5) (JD) 78.125 = 57–1–2 / 8 78.875 = 85 – 7×7/8 (JD) 79.875 = 97 × 7 / 8 – 5 (JD) 81.875 = -8-1 + 87 – 5 (JD) 83.125 = (5 – 1/2)3 – 8 (JD) 83.875 = (7 + 5/8) × (3+8) (JD) 84.375 = (7 + 4/8)3 / 5 (JD) 86.125 = (2+1)6 / 8 – 5 (JD) 86.375 = 635/8 + 7 (JD) 86.875 = 87 – (6–5)/8 (JD) 88.375 = (8 + 5 – 3/8) × 7 (JD) 89.375 = 9×(3+7) – 5/8 (JD) 89.875 = 78 + 95/8 (JD) 91.125 = (9/(1+1))–2+5 (JD) 91.325 = (9/2)3 + 1/5 (JD) 91.875 = (91/8 + 7) × 5 (JD) 92.125 = (9/2)5–2 + 1 (JD) 92.875 = (752 – 9) / 8 (JD) 96.875 = 97 – (6–5)/8 (JD) 97.375 = 779 / (3+5) (JD) 98.375 = (9+5)×7 + 3/8 (JD) 98.875 = (9/8 + 8 + 5) × 7 (JD) 99.875 = 9 × 95 / 8 – 7 (JD) 125.44 = (14 × 4 / 5)2 (JD) 128.75 = 27 + (5+1)/8 (JD) 129.75 = (29 + 7) / (5–1) (JD) 132.25 = 232 / (5–1) (JD) 141.75 = 571 / 4 – 1 (JD) 142.75 = (572 – 1) / 4 (JD) 144.25 = 54 / 4 – 12 (JD) 146.25 = 65 × (2 + 1/4) (JD) 146.75 = 615 / 4 – 7 (JD) 148.75 = 1/4 × 7 × 85 (JD) 154.25 = 55–1 / 4 – 2 (JD) 156.25 = 56–2 / (5–1) (JD) 163.84 = 46 / (3×8+1) (JD) 166.75 = 667 / (5–1) (JD) 169.75 = 679 / (5–1) (JD) 182.25 = (8 + 5 + 1/2)2 (JD) 199.75 = 799 / (5–1) (JD) 204.8 = 84 / 20 (JD) 241.56 = (4 – 5-2) × 61 (JD) 242.75 = (7–4)5 – 2-2 (JD) 243.05 = 35 + 2/40 (JD) 243.25 = 35 + 22–4 (JD) 243.5 = 2 / 4 + 35 (JD) 250.25 = 2-2 + 5 × 50 (JD) 253.44 = 43 × (4 – 5-2) (JD) 255.84 = 28 – 4/5/5 (JD) 262.44 = (6-4 – 4-2)-2 (JD) 272.25 = ((7×5 – 2)/2)2 (JD) 278.25 = (8×5 – 2-2) × 7 (JD) 281.25 = (8 – 1/2)2 × 5 (JD) 286.56 = 6 × 6 × (8 – 5-2) (JD) 288.75 = (2/8 + 8) × 7 × 5 (JD) 295.25 = 2-2 + 59×5 (JD) 295.84 = ((94 – 8)/5)2 (JD) 297.25 = (5×7/2)2 – 9 (JD) 299.5 = 599 / 2 (JD) 306.25 = (6 + 2-3) × 50 (JD) 312.5 = 51+3 / 2 (JD) 326.5 = 653 / 2 (JD) 328.45 = (38 / 4 + 2) / 5 (JD) 328.56 = (8 – 3/5)2 × 6 (JD) 341.75 = 73 – 5/4×1 (JD) 342.25 = (5×4 – 3/2)2 (JD) 345.96 = (5/93)4–6 (JD) 346.75 = 73 × (6 – 5/4) (JD) 347.25 = 372 /4 + 5 (JD) 364.5 = 35 × 6 / 4 (JD) 368.75 = (73 + 6/8) × 5 (JD) 384.25 = (45 × 3 + 2) / 8 (JD) 408.75 = (80 + 7/4) × 5 (JD) 428.75 = 5/28 × 74 (JD) 429.75 = 9 × (72 – 5/4) (JD) 431.75 = ((7+5)3 – 1) / 4 (JD) 436.75 = 73 × 6 – 5/4 (JD) 437.15 = 37 / 5 – 1/4 (JD) 437.75 = (37 + 7/4) / 5 (JD) 438.75 = (73 + 8) × 5 / 4 (JD) 442.25 = (422 + 5) / 4 (JD) 446.75 = 7×64 – 5/4 (JD) 453.75 = (73 / 4 + 5) × 5 (JD) 462.25 = (6×4 – 5/2)2 (JD) 466.75 = (75 – 4) / 6 / 6 (JD) 467.75 = 67×7 – 5/4 (JD) 483.75 = 387 × 5/4 (JD) 486.25 = (65 + 4) / 2 / 8 (JD) 498.25 = (9×5)2 / 4 – 8 (JD) 498.75 = (98 + 7/4) × 5 (JD) 538.24 = (3×8 – 4/5) ^ 2 (JD) 576.24 = 74 × 6/25 (JD) 688.25 = 8 × (2-5 + 86) (JD) 754.25 = 55 / 4 – 27 (JD) 774.25 = (7–2)5 / 4 – 7 (JD) 781.25 = (7/2 – 1)5 × 8 (JD) 795.24 = 9 × (47/5)2 (JD) 812.25 = ((58–1) / 2)2 (JD) 841.25 = (582 + 1) / 4 (JD) 842.75 = (582 + 7) / 4 (JD) 845.25 = 82 + 55 / 4 (JD) 873.25 = (53 – 2/8) × 7 (JD) 992.25 = (9 + 9×5/2)2 (JD) 1024.5 = (1+0)/2 + 45 (JD) 1166.4 = 66 / (41–1) (JD) 1249.5 = 51 × 49 / 2 (JD) 1282.5 = (1/2 + 28) × 5 (JD) 1296.5 = 1/2 + 69–5 (JD) 1365.4 = (46 + 1/5) / 3 (JD) 1464.1 = 114 / (4+6) 1512.5 = 552 / (1+1) (JD) 1553.6 = (65 – 3) / 5 – 1 (JD) 1554.2 = (4+2)5 / 5 – 1 (JD) 1554.6 = (65 + 1 – 4) / 5 (JD) 1555.2 = (5+2–1)5 / 5 1556.2 = 65 / 5 + 2 – 1 (JD) 1556.6 = (65 + 6 + 1) / 5 (JD) 1556.8 = (65 + 8) / 5 × 1 (JD) 1557.2 = (7–1)5 / 5 + 2 (JD) 1557.6 = (65 + 7) / 5 + 1 (JD) 1562.5 = 1 × 56 / 2 / 5 1563.5 = 3 × 55 / 2 + 1 1680.7 = (8–1)6 / 70 (JD) 1946.5 = (65 + 9 + 1) / 4 (JD) 1959.2 = 992 / 5 – 1 (JD) 2048.5 = (84 + 50) / 2 (JD) 2187.5 = 1/2 + (8–5)7 (JD) 2374.5 = 74 – 53/2 (JD) 2457.6 = 24+7 × 6 / 5 (JD) 2502.5 = 502 + 5/2 (JD) 2677.5 = 765 × 7 / 2 (JD) 2737.5 = 75 × 73 / 2 (JD) 2749.5 = (54 / 2 – 7) × 9 (JD) 2999.5 = 5999 / 2 (JD) 3026.5 = 6053 / 2 (JD) 3125.5 = 2/(1+3) + 55 (JD) 3126.5 = 3/2 + (6–1)5 (JD) 3228.5 = 38 / 2 – 52 (JD) 3269.5 = 6539 / 2 (JD) 3273.5 = 33+5 / 2 – 7 (JD) 3274.8 = 47 / (8–3) – 2 (JD) 3275.4 = (47 + 3) / 5 – 2 (JD) 3276.8 = (6–2)7 / (8–3) (JD) 3277.4 = (47 + 3) / (7–2) (JD) 3278.4 = (47 + 8) / (2+3) (JD) 3278.5 = 38 / 2 + 5 – 7 (JD) 3280.5 = 38 / 2 + 0 × 8 3281.5 = 38 / 2 + 15 (JD) 3285.5 = (38 + 5 + 5) / 2 (JD) 3296.5 = 6593 / 2 (JD) 3429.5 = (9/2 + 5)3 × 4 (JD) 3515.2 = (25+1)3 / 5 (JD) 3516.2 = 263 / 5 + 1 (JD) 3578.4 = (83 – 4/5) × 7 (JD) 3627.5 = (36 – 7/2) × 5 (JD) 3642.5 = (36 – 2/4) × 5 (JD) 3646.5 = 36 × 5 + 6/4 (JD) 3935.2 = (39 + 3) / 5 – 2 (JD) 3936.5 = (39 – 3/6) / 5 (JD) 3937.2 = (39 + 3) / (7–2) (JD) 3938.2 = (39 + 8) / (3+2) (JD) 3945.4 = (39 + 44) / 5 (JD) 3954.6 = (94 / 5 + 6) × 3 (JD) 4095.8 = 84 – 90 / 5 (JD) 4096.3 = 46 + 9/30 (JD) 4366.5 = (36 – 5/4) × 6 (JD) 4592.7 = 94 × 7 / 5 / 2 (JD) 4665.2 = (–4 + 66) / 5 / 2 (JD) 4665.6 = 66 / 5 / (6–4) 4685.5 = (55 × 6 – 8) / 4 (JD) 4738.5 = 35 × 78 / 4 (JD) 5529.6 = (2×6)5 / 5 / 9 (JD) 5678.4 = (46 / 5– 8) × 7 (JD) 5734.4 = (4×4)3 × 7 / 5 (JD) 5762.4 = 74 × 2 × 6 / 5 (JD) 5833.6 = (3×6)3 + 8/5 (JD) 5904.9 = 95 / (9+40) 6552.4 = ((2×4)5 – 6) / 5 (JD) 6552.8 = (85 + 2 – 6) / 5 (JD) 6553.6 = (6/3+6)5 / 5 6555.8 = (85 + 6 + 5) / 5 (JD) 6558.4 = (85 + 6×4) / 5 (JD) 7228.5 = 852 + 7/2 (JD) 7649.5 = 94 × 7 / 6 – 5 (JD) 7776.5 = 7/(7+7) + 65 (JD) 7805.5 = 58 / 50 – 7 (JD) 7812.5 = 1 × 57 / (8+2) 8194.5 = (85 + 9 + 1) / 4 (JD) 8427.5 = (75 + 48) / 2 (JD) 9185.4 = 94 × (8–1) / 5 (JD) 9247.5 = (45 + 7/2) × 9 (JD) 9830.4 = 49 × 3 / 80 (JD) 9832.5 = (39 – 8) / 2 – 5 (JD) 9833.5 = 95 / (3+3) – 8 (JD) 9836.5 = 98–3 / 6 – 5 (JD) 9837.5 = (39 – 8) / (7–5) (JD) 9841.5 = 95 / (14–8)

Here are the known repeating fractional Friedman numbers with repeating decimals with 5 or fewer digits:

Known Repeating Fractional Friedman Numbers
 .00016 = 1/6000 (JD) .0016 = 1 / 600 (JD) .00416 = 0 + 1/(4×60) (JD) .00694 = 0 + 0 + 9 / 64 (JD) .01296 = (1 – 2/9) / 60 (JD) .01584 = 8 / (504+1) (JD) .01653 = (1–5–3)/60(JD) .016 = 1 / 60 (JD) .02439 = 2 / (90 + 34) (JD) .03321 = 1/(3–2+30)(JD) .0416 = 0 + 4-1 / 6 (JD) .04583 = (5 – 4/3) / 80 (JD) .04629 = 60 / (9×4)2 (JD) .0694 = 90 / 64 (JD) .1296 = (1–2/9) / 6 (JD) .14287 = ((8+2)–4+1)/7(JD) .14364 = 6/(41 × (4–3)) (JD) .14583 = (5+3–1)/48 (JD) .1653 = (1 – 5-3) / 6 (JD) .16592 = (1–(5–2)/9)/6(JD) .16 = 1 / 6 .17073 = 7/(71–30) (JD) .17592 = (2 + 1/9) / (7+5) (JD) .21296 = (2 – 1/(2×6))/9 (JD) .21951 = 1/(25 / 9 + 1) (JD) .22916 = 22 / 96 × 1 (JD) .25694 = 4/9 – 6/25 (JD) .26829 = 2/(8–6/(2+9)) (JD) .26851 = 58 / 62+1 (JD) .28472 = 82 / 4 / 72 (JD) .28574 = ((5–4)/8+2)/7(JD) .29268 = 6 / (9/2 + 2×8) (JD) .32407 = 70 / (2+4)3 (JD) .34027 = (3×4/7)0–2 (JD) .34146 = (3×6–4)/41 (JD) .34259 = (5/4 – 2/9) / 3 (JD) .35416 = 51 / 36 / 4 (JD) .36585 = 5 / (8/3 + 5 + 6) (JD) .37962 = (3/2 + 7/9) / 6 (JD) .39583 = (3 – 5/8) / (9–3) (JD) .42361 = 61 / (3×4)2 (JD) .43902 = 4 / (9 + 30–2) (JD) .4583 = (5–4/3) / 8 (JD) .47083 = (4 – 7/30) / 8 (JD) .47916 = (4 – 9/(1+7)) / 6 (JD) .48863 = (46–3)/88 (JD) .54629 = (5 – 2/4/6)/9 (JD) .54729 = 4 / ((5/9)2+7) (JD) .55395 = 5/9–(5–3)/5(JD) .55629 = ((5–2)/6+5)/9(JD) .57638 = (5 – 7/6/3) / 8 .58536 = 3 / (5 + (6–5)/8) (JD) .60185 = 65 / 108 (JD) .63194 = 3/16 + 4/9 (JD) .63414 = 4 / (6 + 4/13) (JD) .64583 = (5 + (4–3)/6) / 8 (JD) .65972 = 6/9–(7+5)–2(JD) .66592 = (6–(5–2)/6)/9(JD) .67592 = (7/2 + 5/9) / 6 (JD) .68292 = (9×6+2) / 82 (JD) .73648 = (6 – 4/37) / 8 (JD) .74583 = 7/48 + 3/5 (JD) .76851 = (5 – 7/18) / 6 (JD) .79674 = 7 / (9 – 6/7/4) (JD) .79861 = 7/9 + (8×6)–1 (JD) .82926 = 2 – 96/82 (JD) .85227 = (8–2)/(7+5–2)(JD) .85416 = (5 + 14 / 8) / 6 (JD) .87962 = (7 + 2/9/6) / 8 (JD) .88712 = 1/(8/7–8–2)(JD) .89583 = (8 – 5/(9–3)) / 8 (JD) .89814 = (8 + 1/(4+8)) / 9 (JD) .9583 = 5 / 8 + 3 / 9 (JD) .96527 = 6/25 + 7/9 (JD) .97916 = (7 – 9/(9–1)) / 6 (JD) .98863 = (93 – 6) / 88 (JD) 1.2297 = 91 / (72+2) (JD) 1.3148 = (4–1/18)/3(JD) 1.3472 = 1/72 + 4/3 (JD) 1.4583 = (1+4–5/8)/3 (JD) 1.4861 = (6 – 1/18) / 4 (JD) 1.5416 = (1 + 5 + 1/6) / 4 (JD) 1.694 = 61 / (4×9) 1.7925 = (9 – 1/27) / 5 (JD) 1.7954 = 79/(45–1)(JD) 1.8194 = 11/8 + 4/9 (JD) 1.9861 = (16–1/9)/8(JD) 2.227 = 72 / 22 (JD) 2.2916 = (9+1/6) / (2+2) (JD) 2.4583 = (2×4–5/8)/3 (JD) 2.5416 = (2×5 + 1/6) / 4 (JD) 2.638 = 8 / 3 – 6-2 (JD) 2.9027 = 209 / 72 (JD) 2.9861 = 6/2–1/9/8(JD) 3.2916 = 2–3+19/6(JD) 3.4629 = 4–(2/9+3)/6(JD) 3.5416 = (3 – 1/6) × 5 / 4 (JD) 3.5493 = (4 – 9/5)3 / 3 (JD) 3.5629 = (6/5–9–2)×3(JD) 3.6586 = ((8+6) / 5)3 / 6 (JD) 3.7916 = 91 / 6 / (7–3) 3.7962 = (6/9)3+7/2(JD) 3.8194 = 4 – 13/8/9 (JD) 3.8472 = 4 – (3+8)/72 (JD) 3.9583 = 3 / 9 + 5 / 8 + 3 (HH) 3.9740 = 4 – 7/9/30 (JD) 3.9814 = 4 – 3/9/18 (JD) 3.9861 = (36–1/8)/9(JD) 4.1756 = 5 – 61/74 (JD) 4.2916 = 2 + (9 + 1/6)/4 (JD) 4.4259 = 9/2 – 4/54 (JD) 4.4729 = (9 – 4/74) / 2 (JD) 4.6573 = 7/6×(4–5–3)(JD) 4.7083 = (40–7/3)/8(JD) 4.7638 = 73 / 6 / (8+4) (JD) 4.7916 = 7 – (9–1/6)/4 (JD) 4.7954 = 5–9/4/(7+4)(JD) 4.7962 = (42+7/6)/9(JD) 4.9861 = 46/9–1/8(JD) 5.2638 = 6–3–2+5/8(JD) 5.4629 = 6–29/54(JD) 5.4729 = 92 × 5 / 74 (JD) 5.6527 = 6 – 5×5/72 (JD) 5.7962 = (7×5–2/9)/6(JD) 5.9672 = 6 – 9/275 (JD) 5.9861 = 6–15/9/8(JD) 6.0016 = 600–1+6(JD) 6.016 = 60-1 + 6 (JD) 6.5416 = 5 + (6+1/6)/4 (JD) 6.7592 = 7 – (2–5/9)/6 (JD) 6.7954 = 7–9/4/(6+5)(JD) 6.9814 = (41 + 8/9) / 6 (JD) 6.9973 = 7 – 9/(9+6)3 (JD) 7.7954 = 49/(7–5/7)(JD) 7.8472 = 8 – (7+4)/72 (JD) 8.5694 = 65/8 + 4/9 (JD) 8.7916 = (71 – 6/9) / 8 (JD) 8.9916 = 9 – 1/8/(6+9) (JD) 8.9973 = 9 – 9/(7+8)3 (JD) 9.6527 = 695 / 72 (JD) 9.6851 = (58 + 1/9) / 6 (JD) 12.703 = ((1+2)/7)0–3 (JD) 13.257 = 2/(5–3+1/7)(JD) 13.416 = 161 / 3 / 4 (JD) 13.703 = 1 + (3/7)0–3 (JD) 13.837 = 1 × 83 / 37 (JD) 14.583 = (3 – 1/(4+8))×5 (JD) 14.916 = -1 / 4 + 91 / 6 (HH) 15.972 = 9+7–(5+1)–2(JD) 16.016 = 1 / 60 + 16 (HH) 16.972 = 9–6–2+7+1(JD) 17.361 = (3 + 7/6)1+1 (JD) 18.962 = (8/(9–6))2+1 (JD) 22.361 = (1–6–2)×23(JD) 23.370 = (3–2+70)/3(JD) 23.837 = (8 – 2/37) × 3 (JD) 23.916 = (9–6–2–1)×3(JD) 23.962 = (6+2–9–2)×3(JD) 23.986 = (8–(9+6)–2)×3(JD) 24.296 = ((2/9)2 + 4) × 6 (JD) 25.626 = (62/5)2 / 6 (JD) 25.627 = 6–2+27/5(JD) 25.671 = (76/15)2 (JD) 26.694 = (6 – (9–4)/6)2 (JD) 26.916 = (6×9 – 1/6) / 2 (JD) 27.037 = 730 / 27 (JD) 27.407 = 740 / 27 (JD) 27.416 = (4 – 1/2/6) × 7 (JD) 28.194 = 28 / 9 – 1/4 (JD) 28.583 = 85/3 + 2/8 (JD) 28.653 = (86–5–2)/3(JD) 29.638 = 89/3–6–2(JD) 32.148 = (8+3–(2+1))×4(JD) 32.703 = 20 + (7/3)3 (JD) 33.148 = (8+3–3)×4+1(JD) 34.027 = (70/3/4)2 (JD) 34.583 = 5 × 83 / 4 / 3 (JD) 35.037 = 5×7 + 30–3 (JD) 35.945 = 9×4 – 3/55 (JD) 35.962 = 62 – 9/35 (JD) 36.296 = 62 + (6/9)3 (JD) 37.037 = (70/3/7)3 (JD) 39.740 = 40 – 7/3/9 (JD) 42.583 = (45 – 2) / 3 / 8 (JD) 48.296 = (4/92 + 8) × 6 (JD) 48.583 = 583 / (4+8) (JD) 53.962 = 9×6 – 32–5 (JD) 60.972 = 70–9+6–2(JD) 61.297 = 9×7/(6–2+1)(JD) 61.972 = 71–9+6–2(JD) 62.972 = –(6–2+9–72)(JD) 63.518 = (1 + 8/6)3 × 5 (JD) 63.83 = 383 / 6 (JD) 63.962 = 26 – 36–9 (JD) 63.972 = 73–9+6–2(JD) 64.972 = 74–9+6–2(JD) 65.027 = 6–2+70–5(JD) 65.972 = 9–6–2+57(JD) 66.972 = 76–9+6–2(JD) 67.972 = 77–9+6–2(JD) 68.972 = 78–9+6–2(JD) 69.703 = 70 – (6/9)3 (JD) 69.972 = 79–9+6–2(JD) 78.361 = (6–3+1)×78(JD) 85.326 = (83–5–2)/6(JD) 86.972 = 9–6–2+78(JD) 87.573 = (38 + 7) / 75 (JD) 103.3 = 310 / 3 (JD) 127.83 = 27 – 3/18 (JD) 135.83 = 815 / (3+3) (JD) 167.83 = -1 / 6 + 7 × 8 × 3 (HH) 247.3 = 742 / 3 (JD) 255.36 = 532 / (5+6) (JD) 256.83 = 83 / 2 + 5/6 (JD) 273.06 = 26+7 / 30 (JD) 273.38 = (3–2+37)/8(JD) 364.08 = 48 / 6 / 30 (JD) 397.63 = 93 / (3 – 7/6) (JD) 431.6 = (64–1) / 3 (JD) 432.6 = (64+2) / 3 (JD) 496.48 = 84 / (6 + 9/4) (JD) 511.83 = – (5+1)–1 + 83 (JD) 516.83 = 5 – 1/6 + 83 (JD) 520.83 = 58–2 / 30 (JD) 546.73 = (47 / 6 + 3) / 5 (JD) 563.83 = ((3×5)3 + 8) / 6 (JD) 639.83 = 3839 / 6 (JD) 655.93 = (39 – 5) / 6 / 5 (JD) 662.83 = (632 + 8) / 6 (JD) 677.83 = 83 × 7 × 7 / 6 (JD) 682.6 = (8/2)6 / 6 729.38 = (7/2 + 38) / 9 (JD) 729.63 = 7/(2+9) + 36 (JD) 744.72 = 47 / (7+4) / 2 (JD) 853.3 = 83 × 5 / 3 (JD) 1003.3 = 3010 / 3 (JD) 1024.6 = 210 + 4/6 (JD) 1237.3 = 3712 / 3 (JD) 1294.6 = 64 – 12/9 (JD) 1362.3 = 213 / 6 – 3 (JD) 1364.3 = (46 – 3) / 3 × 1 (JD) 1365.3 = (5–3)13 / 6 1457.3 = 7 × 54 / 3 – 1 (JD) 1458.3 = 54 × (8–1) / 3 (JD) 1819.4 = 48–1 / 9 – 1 (JD) 2185.3 = ((2+1)8 – 5) / 3 (JD) 2238.3 = 822 / 3 – 3 (JD) 2241.3 = (41×2)2 / 3 (JD) 2296.8 = 28×(9–6–2)(JD) 2368.4 = (46 + 8/3)2 (JD) 2397.4 = 74 – 32/9 (JD) 2433.7 = (4/3×37)2(JD) 2439.1 = (14×2)3/9(JD) 2439.6 = ((9+2)4–3)/6 2497.3 = 7492 / 3 (JD) 2725.6 = (2+2)7 / 6 – 5 (JD) 2728.6 = (8/2)7 / 6 – 2 (JD) 2730.6 = (3+20)7 / 6 2731.6 = 27+6 / 3 + 1 (JD) 2732.6 = 27+6 / 3 + 2 (JD) 2733.6 = 27+6 / 3 + 3 (JD) 2734.6 = 27+6 / 3 + 4 (JD) 2735.6 = 27+6 / 3 + 5 (JD) 2736.6 = 27+6 / 3 + 6 (JD) 2737.6 = 27+6 / 3 + 7 (JD) 2738.6 = 27+6 / 3 + 8 (JD) 2739.6 = 27+6 / 3 + 9 (JD) 2758.3 = 8275 / 3 (JD) 2829.3 = 922 / 3 + 8 (JD) 2857.3 = 8572 / 3 (JD) 2916.3 = (9×6)2 + 1/3 (JD) 3125.3 = 1/3 + 52+3 (JD) 3125.6 = 2/3 + (6–1)5 (JD) 3279.3 = (39 – 7) / 2 / 3 (JD) 3279.6 = (39 + 2 – 7) / 6 (JD) 3541.6 = 54 × (6 – 1/3) (JD) 3640.8 = 48 / 3 / (6+0) 3641.8 = 48 / 3 / 6 + 1 (JD) 3642.8 = 48 / 3 / 6 + 2 (JD) 3643.8 = 48 / 3 / 6 + 3 (JD) 3644.8 = 48 / 3 / 6 + 4 (JD) 3645.8 = 48 / 3 / 6 + 5 (JD) 3646.8 = 48 / 3 / 6 + 6 (JD) 3647.8 = 48 / 3 / 6 + 7 (JD) 3648.8 = 48 / 3 / 6 + 8 (JD) 3649.8 = 48 / 3 / 6 + 9 (JD) 3658.3 = (36 + 8/3) × 5 (JD) 3658.6 = 563 / 8 / 6 (JD) 3754.6 = 45 × (6 – 7/3) (JD) 3927.1 = (9×7 – 1/3)2 (JD) 4095.8 = 84 – 50 / 9 (JD) 4096.1 = 46 + 1/9 + 0 (JD) 4096.2 = 46 + 2/9 + 0 (JD) 4096.3 = 46 + 3/9 + 0 (JD) 4096.4 = 46 + 4/9 + 0 (JD) 4096.5 = 46 + 5/9 + 0 (JD) 4096.6 = 46 + 6/9 + 0 (JD) 4096.7 = 46 + 7/9 + 0 (JD) 4096.8 = 46 + 8/9 + 0 (JD) 4098.2 = 84 + 20/9 (JD) 4372.6 = (37 – 4/6) × 2 (JD) 4378.6 = (38 + 7) × 4/6 (JD) 4761.3 = (134 + 7) / 6 (JD) 4769.6 = 46 × 7 / 6 – 9 (JD) 4786.6 = 46 × 7 / 6 + 8 (JD) 4873.3 = (3+8)4 / 3 – 7 (JD) 5206.3 = 56 / 3 – 2 + 0 (JD) 5208.3 = 5–2+0+8 / 3 5327.3 = 732 – 5/3 (JD) 5461.3 = 4(6+15) / 3 5464.3 = (4+4)5 / 6 + 3 (JD) 5465.3 = (5+3)5 / 6 + 4 (JD) 5468.3 = 85 / 6 + 4 + 3 (JD) 5577.3 = (75 – 75) / 3 (JD) 5586.3 = 85 / 6 + 53 (JD) 5597.3 = 75 × 3 / 9 – 5 (JD) 5602.3 = (6+30)5 / 3 5826.7 = (75 + 8/6)2 (JD) 5833.6 = 36 × 8 + 5/3 (JD) 6402.6 = (20–6)4 / 6 (JD) 6485.3 = 45 × 38 / 6 (JD) 6539.3 = (–65 + 39) / 3 (JD) 6947.5 = (56 + 7) × 4 / 9 (JD) 6952.4 = (56 / 9 + 2) × 4 (JD) 7469.7 = 76 × 4 / 9 / 7 (JD) 8362.6 = (63 + 8)2 / 6 (JD) 8738.6 = 8 × (–7 + 38) / 6 (JD) 9216.3 = 962 + 1/3 (JD) 9855.6 = (95 + 85) / 6 (JD)

Bryce Herdt noted that redundant Friedman numbers have to use exponentiation, since that's the only way the output can have more digits than the input. Here are the smallest-known redundant Friedman numbers whose missing sets contain 2 or fewer digits.

Smallest-Known
Redundant Friedman Numbers
withoutnot necessarily nicenice
{0}2048 = 84 / 259052 = 5 + 95 – 2 (BH)
{1}2916 = (9 × 6)23125 = (3 + 2)5
{2}13823 = -1 + (3 × 8)3 (JD)13823 = -1 + (3 × 8)3 (JD)
{3}1331 = 11315623 = 1 + 56 – 3 (BH)
{4}1024 = 2103645 = 36 × 5 (BH)
{5}15552 = (1 + 5)5 × 2 (JD)15552 = (1 + 5)5 × 2 (JD)
{6}15624 = -1 + 52+4 (JD) 15624 = -1 + 52+4 (JD)
{7}3375 = (3 × 5)315627 = 1 × 56 + 2 (BH)
{8}2187 = (2 + 1)72187 = (2 + 1)7
{9}4096 = (4 + 0)64096 = (4 + 0)6

withoutnot necessarily nicenice
{0,0}125000 = 502+1 (BH)1048608 = 1 × 4 × (86 + 8) (JD)
{0,1}105625 =(65 × 5)2 (JD)156250 = 56 × 2 × 5 (JD)
{0,2}32805 = 38 × 5 (BH)32805 = 38 × 5 (BH)
{0,3}131072 = 1 × 217 (BH)380538 = 38 × 58 (JD)
{0,4}59054 = 5 + 95 (BH)59054 = 5 + 95 (BH)
{0,5}59045 = 95 – 4 (JD)59049 = 9–4+9
{0,6}46660 = 4 + 6646660 = 4 + 66
{0,7}104976 = 16 × 94 (JD)470576 = 4 × (-5 + 76) (JD)
{0,8}16807 = 76–11048575 = -1 + (4 + 5 + 7 )5 (JD)
{0,9}4096 = 464096 = 46
{1,1}11664 = 66 / 411664 = 66 / 4
{1,2}132651 = 516–3 (BH)147492 = (47 + 4) × 9 (JD)
{1,3}15623 = 56 – 215623 = 56 – 2
{1,4}46651 = 66 – 546651 = 66 – 5
{1,5}117568 = -81 + 76 (JD)117645 = 1 × 76 – 4 (BH)
{1,6}117636 = -13 + 76 (JD)117646 = 1 + 76 – 4 (BH)
{1,7}15627 = 56 + 215627 = 56 + 2
{1,8}13824 = 243 (BH)279841 =(2 × 7 + 9)4 (JD)
{1,9}117649 =76 × 14 (JD)1397493 = 39 × (7 + 43) (JD)
{2,2}248832 = (4 + 8)8–3 (BH) 248832 = (4 + 8)8–3 (BH)
{2,3}229376 =7 × 29+6 (JD)262138 = -6 + 218 (JD)
{2,4}15624 = -1 + 5615624 = -1 + 56
{2,5}15625 = 1 × 5615625 = 1 × 56
{2,6}15625 = 55+1 (JD)15626 = 1 + 56
{2,7}78125 = 58–1 (JD)912673 = (91 + 6)3 (JP)
{2,8}78125 = 57×1 (JD) 186624 = 1 × 66 × 4 (JD)
{2,9}279933 = (9 – 3)7 – 3 (JD)1679621 = (1 + 67) × 6 – 1 (JD)
{3,3}238336 = 8 + 623 (JD)373239 = 723 – 9 (JD)
{3,4}234248 = 224 – 8 (JD)234248 = 224 – 8 (JD)
{3,5}234253 = 224 – 3 (JD)354375 = (3 × 5)4 × 7 (JD)
{3,6}16384 = 48–132768 = 27+8
{3,7}537824 = (8 + 4 + 2)5 (JD)1127357 = (-1 + 12)5 × 7 (JD)
{3,8}16384 = 41+6117638 = -11 + 76 (JD)
{3,9}279936 = ((9 – 6) × 2)7 (JD)1399675 =(-19 + 67) × 5 (JD)
{4,4}46648 = 66 – 8 (JD) 46648 = 66 – 8 (JD)
{4,5}46653 = 66 – 346653 = 66 – 3
{4,6}14641 = 11446656 = 65 × 6
{4,7}117647 = -1 – 1 + 76 (BH)117647 = -1 – 1 + 76 (BH)
{4,8}24389 = 293 (JD)117648 = -1 × 1 + 76 (BH)
{4,9}59049 = 95 + 0117649 = 1 × 1 × 76 (BH)
{5,5}458751 = 48 × 7 – 1 (JD)458751 = 48 × 7 – 1 (JD)
{5,6}585336 = 583 × 3 (JD)585336 = 583 × 3 (JD)
{5,7}166375 = (-6 + 61)3 (JD)458752 = 48 × (5 + 2) (JD)
{5,8}458748 =- 4 + 7 × 48 (JD)458748 =- 4 + 7 × 48 (JD)
{5,9}234259 = 224 + 3 (JD)470596 = 4 × ((7 + 0)6) (JD)
{6,6}236196 = 12 × 39 (JD)1679613 = (-1 + 7)9–2 – 3 (JD)
{6,7}32768 = 83+2157463 = -1 + 543 (JD)
{6,8}19683 = 1 × 391647086 = 14 × (7 + 0)6 (JD)
{6,9}19683 = 31+81046529 = (-1 + (0 + 4)5)2 (JD)
{7,7}177143 = -4 + 311 (JD)759375 = (5 × 9 / 3)5 (JD)
{7,8}137842 = 413 × 2 (JP)1048575 = -1 + (0 + 4)5+5 (JD)
{7,9}117649 = (-4 + 11)6 (JD)759375 = (7 + 5 + 3)5 (JP)
{8,8}524288 = 45×2 / 2 (JD)1834987 = 1 × (-3 + 49) × 7 (JD)
{8,9}279834 = -7 + 234 (JD)1679586 = (1 × 67 – 5) × 6 (JD)
{9,9}279933 = (3 × 2)7 – 3 (BH)1399675 = (-13 + 67) × 5 (JD)

withoutnot necessarily nicenice
{0,0,0} 6250000 = 506–2 (JD) 10077690 = 17–7+69 (JD)
{0,0,1} 1048580 = (8+8)5+4 (JD) 1048608 = 4×(86+8) (JD)
{0,0,2} 3429500 = 953×4 (JD) 12706092 = 12×(76×9) (JD)
{0,0,3} 300763 = 673 (JD) 10504375 = (1×5)4×(75) (JD)
{0,0,4} 5764800 = 78+5–6 (JD) 10077694 = –1–7/7+69 (JD)
{0,0,5} 2097150 = (–1+9)7–2 (JD) 10077695 = –1+7–7+69 (JD)
{0,0,6} 5764800 = 78+4–5 (JD) 10077693 = (–17+7)9–3 (JD)
{0,0,7} 3375000 = (5×30)3 (JD) 10077688 = (–1+7)×68–8 (JD)
{0,0,8} 10076983 = –713+69 (JD) 10077689 = 17×(–7+69) (JD)
{0,0,9} 2097088 = 87–82 (JD) 10077696 = (–1+7)7×6×6 (JD)
{0,1,1} 1953102 = –23+59 (JD) 10077619 = 0–77+69 (JD)
{0,1,2} 1950724 = 59–74 (JD) 2097152 = 29+7+5 (JD)
{0,1,3} 131072 = 217 (JD) 4194304 = 49×(4×4) (JD)
{0,1,4} 1176490 = 76×(9+1) (JD) 4194304 = (49+3)/4 (JD)
{0,1,5} 117650 = 1+76 (JD) 117650 = 1+76 (JD)
{0,1,6} 161051 = 115 (JD) 161051 = 115 (JD)
{0,1,7} 781250 = 58×2 (JD) 1679608 = 69/6–8 (JD)
{0,1,8} 1048584 = 8+(4×4)5 (JD) 1075648 = 75×64 (JD)
{0,1,9} 1048596 = (86+5)×4 (JD) 1679608 = 67×6–8 (JD)
{0,2,2} 2097152 = (9–15)7 (JD) 20155392 = (–1+5)5×39 (JD)
{0,2,3} 8203125 = 21×(58) (JD) 11390626 = 1+(1×(9+6))6 (JD)
{0,2,4} 2097146 = (–1+9)7–6 (JD) 4782970 = –7+8+97 (JD)
{0,2,5} 2097151 = (–1+9)7–1 (JD) 11390625 = ((1+1)×3+9)6 (JD)
{0,2,6} 2085136 = 385–1 (JD) 6298560 = 69/(8/5) (JD)
{0,2,7} 205379 = 593 (JD) 2097152 = (9–1)5+2 (JD)
{0,2,8} 1062882 = ((8+1)6)×2 (JD) 5242880 = 5×(42+8) (JD)
{0,2,9} 2097148 = 87–4×1 (JD) 2097152 = (7+1)5+2 (JD)
{0,3,3} 11390634 = 9+(4+11)6 (JD) 11390636 = 11+(9+6)6 (JD)
{0,3,4} 1953064 = –61+59 (JD) 4194304 = (41+9)×4 (JD)
{0,3,5} 5308416 = (8×6)4×1 (JD) 10485735 = (–1–4+87)×5 (JD)
{0,3,6} 3906250 = 59×(2+0) (JD) 3906259 = 9+2×(59) (JD)
{0,3,7} 1073733 = 713×3 (JD) 10077693 = –10+7+69 (JD)
{0,3,8} 1953084 = –41+59 (JD) 8388608 = 88/(–6+8) (JD)
{0,3,9} 390625 = 56+2 (JD) 4980736 = 48×76 (JD)
{0,4,4} 4194304 = 4-1+9+3 (JD) 4194304 = 4-1+9+3 (JD)
{0,4,5} 2097154 = (9–1)7+2 (JD) 10485745 = (1–4+87)×5 (JD)
{0,4,6} 1048576 = (8+7+1)5 (JD) 5764803 = 5+78–3 (JD)
{0,4,7} 1048576 = 86×(5–1) (JD) 14348907 = (–1+4)3×8–9 (JD)
{0,4,8} 468750 = 57×6 (JD) 13845840 = –1+(3+58)4 (JD)
{0,4,9} 59049 = 95 (JD) 4194304 = 4–(1–3×4) (JD)
{0,5,5} 5038856 = 8+68×3 (JD) 10485755 = (1+4)×(87)–5 (JD)
{0,5,6} 1048576 = (87–1)×4 (JD) 10485756 = 1×(–4+87×5) (JD)
{0,5,7} 1048576 = 1×4×86 (JD) 1048576 = 1×4×86 (JD)
{0,5,8} 1048576 = ((7+1)6)×4 (JD) 10485785 = (1+4+87)×5 (JD)
{0,5,9} 470596 = 4×(76) (JD) 470596 = 4×(76) (JD)
{0,6,6} 3906256 = (59+3)×2 (JD) 10077696 = (–1+07+7)9 (JD)
{0,6,7} 1048576 = (85+1)×4 (JD) 1679608 = 1–9+68 (JD)
{0,6,8} 1647086 = 14×(76) (JD) 1647086 = 14×(76) (JD)
{0,6,9} 390625 = 523 (JD) 1046529 = (1–45)2 (JD)
{0,7,7} 4477460 = 464+4 (JD) 10077679 = –10–7+69 (JD)
{0,7,8} 1048575 = –1+45+5 (JD) 1048575 = –1+45+5 (JD)
{0,7,9} 3748096 = (8+36)4 (JD) 10077699 = 10–7+69 (JD)
{0,8,8} 5859380 = 5+59×3 (JD) 5859380 = 5+59×3 (JD)
{0,8,9} 5859390 = (5+59)×3 (JD) 5859390 = (5+59)×3 (JD)
{0,9,9} 24009975 = 704–52 (JD) 60459696 = 64×(–5+66) (JD)
{1,1,1} 1171875 = 57×(8+7) (JD) 1953116 = –9+53+6 (JD)
{1,1,2} 1953112 = –13+59 (JD) 12387168 = (3/8+7)×(68) (JD)
{1,1,3} 1419853 = –4+(9+8)5 (JD) 1419853 = –4+(9+8)5 (JD)
{1,1,4} 117654 = 76+5 (JD) 117654 = 76+5 (JD)
{1,1,5} 117645 = 76–4 (JD) 117645 = 76–4 (JD)
{1,1,6} 1179648 = 47×(9×8) (JD) 1679616 = 6-7+9+6 (JD)
{1,1,7} 1679613 = 69/6–3 (JD) 1679613 = 69/6–3 (JD)
{1,1,8} 1594318 = 39+4–5 (JD) 13845841 = (3–4–(5–8))4 (JD)
{1,1,9} 1679581 = 68–7×5 (JD) 1679613 = 67×6–3 (JD)
{1,2,2} 262144 = (4+4)6 (JD) 12582762 = (–25+87)×6 (JD)
{1,2,3} 1594323 = 94×(35) (JD) 11390626 = 1+(9+0+6)6 (JD)
{1,2,4} 262144 = (4×2)6 (JD) 2313441 = (3×13)4 (JD)
{1,2,5} 15625 = 56 (JD) 15625 = 56 (JD)
{1,2,6} 132651 = 513 (JD) 912673 = 973 (JD)
{1,2,7} 1692738 = 86×(39) (JD) 16777216 = 16-7+7+6 (JD)
{1,2,8} 78125 = 57 (JD) 186624 = 66×4 (JD)
{1,2,9} 1952396 = 59–36 (JD) 1953125 = 53+1+5 (JD)
{1,3,3} 1594323 = (5–2)9+4 (JD) 3816336 = 863×6 (JD)
{1,3,4} 1439671 = (69+1)/7 (JD) 13436888 = (3+68–8)×8 (JD)
{1,3,5} 1594323 = (94+2)×3 (JD) 1594323 = (94+2)×3 (JD)
{1,3,6} 1953126 = 59+2–1 (JD) 8388612 = (88+8)/2 (JD)
{1,3,7} 1953075 = –50+59 (JD) 9437184 = 9×((4×8)4) (JD)
{1,3,8} 1953128 = 59+2+1 (JD) 13436928 = (3×4)6×9/2 (JD)
{1,3,9} 1594323 = 35+4×2 (JD) 1679683 = 67+68 (JD)
{1,4,4} 4782941 = –28+97 (JD) 14314572 = (315–7)/2 (JD)
{1,4,5} 1594323 = 93×2×3 (JD) 1594323 = 93×2×3 (JD)
{1,4,6} 1365784 = 583×7 (JD) 1419856 = –1+(9+8)5 (JD)
{1,4,7} 1419857 = (1×(9+8))5 (JD) 1419857 = (1×(9+8))5 (JD)
{1,4,8} 117648 = –1+76 (JD) 117648 = –1+76 (JD)
{1,4,9} 117649 = (1×7)6 (JD) 117649 = (1×7)6 (JD)
{1,5,5} 1594325 = 39+4+2 (JD) 5859351 = (–8+59)×3 (JD)
{1,5,6} 1953126 = (3+2)9+1 (JD) 3176523 = (3×72)3 (JD)
{1,5,7} 1048576 = (0+4)×(86) (JD) 1048576 = (0+4)×(86) (JD)
{1,5,8} 1419857 = 179–4 (JD) 13845841 = (13+48)4 (JD)
{1,5,9} 357911 = 713 (JD) 1679615 = –1+67×6 (JD)
{1,6,6} 1633689 = 83×(39) (JD) 1679616 = (–1+7)9/6 (JD)
{1,6,7} 1679613 = 69–1–3 (JD) 1679613 = 69–1–3 (JD)
{1,6,8} 19683 = 39 (JD) 3188646 = (38+4)×6 (JD)
{1,6,9} 1562498 = 58×4–2 (JD) 1679613 = 67+1–3 (JD)
{1,7,7} 1679617 = 1+69/6 (JD) 1679617 = 1+69/6 (JD)
{1,7,8} 1048571 = –5+410 (JD) 3145728 = 3×(45×2) (JD)
{1,7,9} 1679586 = 68–6×5 (JD) 1679616 = (66+1)×6 (JD)
{1,8,8} 1048581 = 5+410 (JD) 1834987 = (–3+49)×7 (JD)
{1,8,9} 1193859 = 9×(513) (JD) 1679586 = (67–5)×6 (JD)
{1,9,9} 1952997 = 59–27 (JD) 39135390 = 335–3+0 (JD)
{2,2,2} 22425763 = (47×6)3–5 (JD) 96722262 = 96×(7×26) (JD)
{2,2,3} 12252303 = 215×(3+0) (JD) 22851963 = (–8+51)×96 (JD)
{2,2,4} 295245 = 95×5 (JD) 295245 = 95×5 (JD)
{2,2,5} 524288 = 48×8 (JD) 524288 = 48×8 (JD)
{2,2,6} 12362256 = 35162 (JD) 28697822 = (–2+8)×97+8 (JD)
{2,2,7} 1679622 = 69–1+6 (JD) 38263728 = (38+6–3)×8 (JD)
{2,2,8} 2458624 = 564/4 (JD) 4782972 = –4+7+97 (JD)
{2,2,9} 1679622 = (1+67)×6 (JD) 1679622 = (1+67)×6 (JD)
{2,3,3} 1953123 = 59–1–1 (JD) 18874332 = (1+8)×(87–4) (JD)
{2,3,4} 234375 = 57×3 (JD) 14823772 = 18×(77)–2 (JD)
{2,3,5} 1594323 = 3(9+4)×1 (JD) 20155392 = 2×((0+1+5)9) (JD)
{2,3,6} 1679623 = 69–1+7 (JD) 24634368 = 44/(3/(68)) (JD)
{2,3,7} 1127357 = 115×7 (JD) 1127357 = 115×7 (JD)
{2,3,8} 3748322 = 374×2 (JD) 3748322 = 374×2 (JD)
{2,3,9} 6235397 = 53×(76) (JD) 13436928 = (1+3+4)×(68) (JD)
{2,4,4} 14348925 = 18+(9×3)5 (JD) 22674814 = –2+67×81 (JD)
{2,4,5} 1572864 = (–1+7)×86 (JD) 1572864 = (–1+7)×86 (JD)
{2,4,6} 4782956 = 97–8–5 (JD) 14276736 = 17×(67×3) (JD)
{2,4,7} 786432 = 86×3 (JD) 786432 = 86×3 (JD)
{2,4,8} 4782957 = 97–7–5 (JD) 4782973 = 7+97–3 (JD)
{2,4,9} 4782969 = 98+6–7 (JD) 13436928 = (–1+3)3×68 (JD)
{2,5,5} 458752 = 48×7 (JD) 458752 = 48×7 (JD)
{2,5,6} 1679625 = 9+67+1 (JD) 15752946 = –15+(7×9)4 (JD)
{2,5,7} 1572864 = (48+1)×6 (JD) 4782957 = –4–8+97 (JD)
{2,5,8} 589824 = 9×(48) (JD) 25165824 = 165×24 (JD)
{2,5,9} 1594323 = 34×3+1 (JD) 7529536 = (7×(5–3))6 (JD)
{2,6,6} 9765625 = 5(9–7)×5 (JD) 16777216 = ((1+7)7)×(7+1) (JD)
{2,6,7} 4782967 = 97–8/4 (JD) 11756723 = 115×73 (JD)
{2,6,8} 4782969 = 949/7 (JD) 26873856 = 68×(7×3–5) (JD)
{2,6,9} 279936 = (9–3)7 (JD) 56953125 = 5×((5×3)1+5) (JD)
{2,7,7} 12671875 = 811×(56) (JD) 16777213 = 167–1–3 (JD)
{2,7,8} 4782927 = –42+97 (JD) 4782927 = –42+97 (JD)
{2,7,9} 12326397 = 6+2313 (JD) 17825792 = 17×((8×2)5) (JD)
{2,8,8} 4826809 = (9+4)6+0 (JD) 28697748 = 6×(97–7–4) (JD)
{2,8,9} 1889562 = 185–6 (JD) 1889562 = 185–6 (JD)
{2,9,9} 2985976 = –8+(7+5)6 (JD) 2985976 = –8+(5+7)6 (JD)
{3,3,3} 33362174 = 764–2×1 (JD) ?
{3,3,4} 4194313 = 9+411 (JD) 13764933 = 13×(76×9) (JD)
{3,3,5} 1594323 = (2+1)9+4 (JD) 24137563 = –2–4+176 (JD)
{3,3,6} 1953136 = 11+59 (JD) 17934936 = (–1+79)×4/9 (JD)
{3,3,7} 2734375 = 7×(54×2) (JD) 37748736 = ((7–4)×(87))×6 (JD)
{3,3,8} 13436888 = (-1–4+68)×8 (JD) 13436888 = (–1–4+68)×8 (JD)
{3,3,9} 3538944 = 54×(48) (JD) 35831799 = (5+8–1)7–9 (JD)
{3,4,4} 1446336 = 31×(66) (JD) 14823774 = ((1+8)×2)×(77) (JD)
{3,4,5} 1594323 = 913/2 (JD) 18874359 = (1+8)×(87)–9 (JD)
{3,4,6} 4782963 = 97+2–8 (JD) 18874364 = (1+8)×(87)–4 (JD)
{3,4,7} 1764735 = 15×(76) (JD) 4782973 = 8/2+97 (JD)
{3,4,8} 373248 = 723 (JD) 3188646 = ((1+8)6)×6 (JD)
{3,4,9} 1397493 = 71×(39) (JD) 4194304 = 410×4 (JD)
{3,5,5} 5345344 = 344×4 (JD) 5345344 = 344×4 (JD)
{3,5,6} 234256 = 224 (JD) 2359296 = 29×2×9 (JD)
{3,5,7} 5859375 = (–5+8)×59 (JD) 5859375 = (–5+8)×59 (JD)
{3,5,8} 4782953 = 97–42 (JD) 5859383 = 8+59×3 (JD)
{3,5,9} 1953125 = 511–2 (JD) 7529536 = (7+2+5)6 (JD)
{3,6,6} 13237696 = 17×(923) (JD) 36756963 = ((3×7)5+6)×9 (JD)
{3,6,7} 3764768 = 4×76×8 (JD) 3764768 = 4×76×8 (JD)
{3,6,8} 4782963 = 97–4–2 (JD) 26873848 = ((2+7)×8)4–8 (JD)
{3,6,9} 12326391 = 2312+1 (JD) 26873968 = (2×(68+7))×8 (JD)
{3,7,7} 11477376 = 41×(67×1) (JD) ?
{3,7,8} 13845796 = 614–9×5 (JD) 26873824 = (–2+68)×24 (JD)
{3,7,9} 279936 = 69–2 (JD) 24137569 = (2+(4–1)×5)6 (JD)
{3,8,8} 13176688 = 16×(76+1) (JD) 26873854 = –2+(6×(7+5))4 (JD)
{3,8,9} 4782973 = 4+(7+2)7 (JD) 4782973 = 4+(7+2)7 (JD)
{3,9,9} 1399675 = (–1+67)×5 (JD) 1399675 = (–1+67)×5 (JD)
{4,4,4} 18874449 = (1+8+87)×9 (JD) 18874449 = (1+8+87)×9 (JD)
{4,4,5} 14556724 = 52×(67+1) (JD) 23914845 = (2+3)/(91–8) (JD)
{4,4,6} 6484375 = 83×(57) (JD) 14349636 = (1+39)×(36) (JD)
{4,4,7} 14172486 = 8×(116)–2 (JD) 14172488 = (11–(2–8))×8 (JD)
{4,4,8} 4478976 = 67×(9+7) (JD) 4782974 = 7–2+97 (JD)
{4,4,9} 11239424 = (2×112)3 (JD) 14348907 = (1×3)8+0+7 (JD)
{4,5,5} 5764795 = 79/7–6 (JD) 10485755 = (–1+0+87)×5 (JD)
{4,5,6} 46656 = 66 (JD) 46656 = 66 (JD)
{4,5,7} 1572864 = 218×6 (JD) 4782975 = 8–2+97 (JD)
{4,5,8} 1048584 = 8+410 (JD) 5764788 = –7–6+78 (JD)
{4,5,9} 1594323 = 3×(312) (JD) 10485759 = –1+0+(87)×5 (JD)
{4,6,6} 5764796 = 79/7–5 (JD) 5764806 = 5+78+0 (JD)
{4,6,7} 4296875 = 58×(9+2) (JD) 5764788 = –5+78–8 (JD)
{4,6,8} 3188646 = 813×6 (JD) 6718464 = (67+1)×4 (JD)
{4,6,9} 4782969 = 98/(7+2) (JD) 5764789 = –5–7+78 (JD)
{4,7,7} 4478976 = (9×8)4/6 (JD) 71744535 = (–1+4)5×3×5 (JD)
{4,7,8} 1048576 = 165+0 (JD) 4782971 = 2+97×1 (JD)
{4,7,9} 1419857 = (–1+18)5 (JD) 1419857 = (–1+18)5 (JD)
{4,8,8} 4782897 = –72+97 (JD) 4782897 = –72+97 (JD)
{4,8,9} 438976 = 763 (JD) 4782969 = ((7+2)6)×9 (JD)
{4,9,9} 12794929 = ((29–1)×7)2 (JD) 69343975 = 6×3+375 (JD)
{5,5,5} 29552654 = (–9+624)×2 (JD) ?
{5,5,6} 5764805 = 78+4+0 (JD) 7529536 = (7×2)9–3 (JD)
{5,5,7} 7529536 = (2+9+3)6 (JD) 7529536 = (2+9+3)6 (JD)
{5,5,8} 13845865 = 614+8×3 (JD) 28697558 = –(28)+6×(97) (JD)
{5,5,9} 5764795 = (7×7)4–6 (JD) 54525952 = 42×5×52 (JD)
{5,6,6} 9765625 = 59×(7–2) (JD) 53366445 = 334×45 (JD)
{5,6,7} 1048576 = (8–4)10 (JD) 1679615 = –1+69–1 (JD)
{5,6,8} 1048568 = –8+410 (JD) 26873856 = (26+8)7–3 (JD)
{5,6,9} 1679615 = –1+67+1 (JD) 1679615 = –1+67+1 (JD)
{5,7,7} 1771556 = 116–5 (JD) 1771561 = 116×1 (JD)
{5,7,8} 1048573 = 410–3 (JD) 4782975 = 4+2+97 (JD)
{5,7,9} 2097152 = 221+0 (JD) 5359375 = (5×35)3 (JD)
{5,8,8} 4782985 = 97+42 (JD) 28697658 = (–26+97)×6 (JD)
{5,8,9} 1419857 = 174+1 (JD) 1889559 = 185–9 (JD)
{5,9,9} 2985984 = (8+4)8–2 (JD) 5859399 = (8+59)×3 (JD)
{6,6,6} 1679616 = (1–7)9–1 (JD) 1679616 = (1–7)9–1 (JD)
{6,6,7} 1679616 = (1×6)9–1 (JD) 1679616 = (1×6)9–1 (JD)
{6,6,8} 9765618 = 59+1–7 (JD) 13176688 = ((13+1)7)/8 (JD)
{6,6,9} 1679616 = (1×6)7+1 (JD) 1679616 = (1×6)7+1 (JD)
{6,7,7} 1679617 = 1+69–1 (JD) 1679617 = 1+69–1 (JD)
{6,7,8} 3796875 = 9×(753) (JD) 4782967 = –4+2+97 (JD)
{6,7,9} 1679616 = 66+1+1 (JD) 1679617 = 1+61+7 (JD)
{6,8,8} 1889568 = (1+8+9)5 (JD) 1889568 = (1+8+9)5 (JD)
{6,8,9} 1889564 = 185–4 (JD) 1889564 = 185–4 (JD)
{6,9,9} 279936 = (3×2)7 (JD) 9834496 = (8×(3+4))4 (JD)
{7,7,7} 10077697 = 1+(0+0+6)9 (JD) 10077697 = 1+(0+0+6)9 (JD)
{7,7,8} 1889577 = 9+185 (JD) 4782977 = 4×2+97 (JD)
{7,7,9} 759375 = (5×3)5 (JD) 759375 = (5×3)5 (JD)
{7,8,8} 13845876 = 35+614 (JD) 28697816 = 2+6×(91+6) (JD)
{7,8,9} 4478976 = 67×(4×4) (JD) 17373978 = –1+(7×37)3 (JD)
{7,9,9} 17373979 = (1×7×37)3 (JD) 17373979 = (1×7×37)3 (JD)
{8,8,8} 14348898 = –9+34×4–1 (JD) 28697818 = –2+6×(97+1) (JD)
{8,8,9} 12837889 = (83×7–1)2 (JD) 75898944 = ((7+59)4)×4 (JD)
{8,9,9} 4782969 = (62/4)7 (JD) ?
{9,9,9} 25599984 = 8×((5×4)5–2) (JD) 999999950 = (9 + 9/9)9 – 50 (BH)

A integer n is called an almost Friedman number if it can be written with the digits of n–1 or n+1, along with the four basic arithmetic operations, exponentiation, and parentheses. Here are the known almost Friedman numbers with 5 or fewer digits.

Almost Friedman Numbers (written with the digits of n–1)
 128 = 1 × 27 570 = 95 × 6 (JD) 1280 = (1 + 9) × 27 1295 = (4 × 9)2 – 1 1296 = (9 × (5 – 1))2 (JD) 1323 = 3 × 212 (JD) 1330 = (2 + 9)3 – 1 1365 = (46 – 1) / 3 1428 = 714 × 2 (JD) 1763 = -1 + (7 × 6)2 1764 = (6 × 7)3–1 2048 = (2 + 0)4+7 2179 = (2 + 1)7 – 8 2187 = (6 / 2)8–1 2368 = 37 × 26 (JD) 2460 = 492 × 5 (JD) 2592 = 512 – 9 (JD) 2688 = 82 × 6 × 7 2744 = (2 / (7 × 4 ))-3 (BH) 2784 = 87 × 32 (JD) 2916 = (9 × (5 + 1))2 2917 = (9 × 6)2 + 1 3156 = 31 + 55 (JD) 3215 = (3 + 2)1+4 3126 = (3 + 2)5 + 1 3579 = 83 × 7 – 5 3600 = (93 – 9) × 5 3603 = 3 + 602 (JD) 3672 = 17 × 63 (JD) 3936 = (39 – 3) / 5 4096 = (9 – 50)4 4097 = 46 + 90 4370 = 93 × 6 – 4 4793 = 74 × 2 – 9 5832 = 31+5 × 8 (JD) 5837 = 5 + 8 × 36 5929 = (9 × 8 + 5)2 5970 = 995 × 6 (JD) 6256 = 6 + 2 × 55 6496 = 94 – 65 (JD) 6550 = 94 – 6 – 5 7776 = (7 – 7 / 7)5 9216 = (95 + 1)2 (JD) 9217 = 962 + 1 (JD) 10239 = 20 × 83 – 1 10240 = 20 × (9 – 1)3 10353 = 203 × 51 10626 = 506 × 21 11025 = (101 + 4)2 11026 = 1052 + 1 11236 = ((1 + 1) × 53)2 11664 = 1 × 66 / (1 + 3) 11665 = 1 + 1 × 66 / 4 12264 = 6132 × 2 12288 = 12 × 8 × 27 12347 = 423 / 6 – 1 12348 = 423 / (7 – 1) 12540 = 132 × 95 12544 = (14 × (3 + 5))2 12549 = (14 × 8)2 + 5 12624 = 6312 × 2 12636 = 52 × 36–1 12696 = 6 × (5 × 9 + 1)2 12800 = (99 + 1) × 27 12996 = (99 + 15)2 13225 = (23 × (1 + 4))2 13226 = (23 × 5)2 + 1 13593 = 591 × 23 13699 = 19 × (36 – 8) 13755 = 5 × (143 + 7) 13824 = ((1+3) × (8–2))3 (BH) 13825 = (2 × (4 + 8))3 + 1 13888 = 31 × 8 × 8 × 7 13924 = (39 × 3 + 1)2 13986 = 518 × 9 × 3 14028 = 7014 × 2 14208 = 7104 × 2 14298 = 7149 × 2 14632 = 114 – 6 – 3 14635 = (3 × 4 – 1)4 – 6 14638 = (17 – 6)4 – 3 14640 = (6 / 3 + 9)4 – 1 14641 = (1 + 4 + 6)4 + 0 14642 = (1 + 4 + 6)4 + 1 14643 = (1 + 4 + 6)4 + 2 14644 = (1 + 4 + 6)4 + 3 14645 = (1 + 4 + 6)4 + 4 14646 = (1 + 4 + 6)4 + 5 14647 = (1 + 4 + 6)4 + 6 14648 = (1 + 4 + 6)4 + 7 14649 = (1 + 4 + 6)4 + 8 14650 = (1 + 4 + 6)4 + 9 14651 = (5 + 6)4 + 10 14652 = (5 + 6)4 + 11 14653 = (5 + 6)4 + 12 14654 = (5 + 6)4 + 13 14655 = 14 + (6 + 5)4 (JD) 14656 = (5 + 6)4 + 15 14657 = (5 + 6)4 + 16 14658 = (5 + 6)4 + 17 14659 = (5 + 6)4 + 18 14660 = (5 + 6)4 + 19 14688 = 864 × 17 14711 = 114 + 70 14712 = 114 + 71 14713 = 114 + 72 14714 = 114 + 73 14715 = 114 + 74 14716 = 114 + 75 14717 = 114 + 76 14718 = 114 + 77 14719 = 114 + 78 14720 = 114 + 79 15129 = (115 + 8)2 15342 = 5114 × 3 15345 = 341 × 45 15355 = 5 × (3 × 45 – 1) 15369 = 56 – (3 – 1)8 15374 = 7 × 133 – 5 15375 = 375 × 41 15376 = (-1 + 53)7–5 (JD) 15379 = 1 × 7 × (5 + 8)3 15435 = 441 × 35 15444 = 351×44 (JD) 15544 = 55+1 – 34 (BH) 15555 = (55 – 14) × 5 15562 = (65 + 5) × (1 + 1) 15563 = (65 + 5) × 2 + 1 15564 = (5 × 5)3 – 61 (BH) 15565 = 56 – 15 × 4 15568 = 56 – 57 × 1 15570 = 591 × 5 × 6 15573 = 57–1 – 52 15580 = 57–1 – 5 × 9 15585 = (1 + 4) × (55 – 8) 15586 = 1 + (55 – 8) × 5 15608 = 56 – 17 + 0 15613 = 1 × 56 – 12 15617 = -1 + 56 – 1 – 6 15618 = 1 × 56 – 1 × 7 15619 = 1 + 56 + 1 – 8 15622 = 1 × 56 – 2 – 1 15623 = -1 + 56 – 2 / 2 15624 = 1 × 56 + 2 – 3 15625 = 56 × 124 (BH) 15626 = 56 + 125 15627 = 56 + 6 / (1 + 2) 15628 = 56 + 2 + 17 15629 = 56 + 12 – 8 15630 = 56 + (1 + 9) / 2 15633 = -1 + 56 + 32 15634 = 1 × 56 + 3 × 3 15637 = 56 + 6 × (3 – 1) 15645 = 56 + 4 × (4 + 1) 15646 = 1 + 56 + 4 × 5 15649 = 56 + 8 × (4 – 1) 15655 = 5 × (51+4 + 6) 15656 = 1 + 5 × (6 + 55) 15667 = 56 + 6 × (6 + 1) 15668 = 1 + 56 + 6 × 7 (BH) 15670 = 56 + 9 × (6 – 1) 15673 = -1 + 56 + 72 15674 = 56 + 73–1 15688 = 56 + 7 × (8 + 1) 15689 = 1 × 56 + 8 × 8 15735 = 3147 × 5 15753 = 51+5 + 27 15988 = 75 – 891 16129 = (16 × 8 – 1)2 16224 = 3122 / 6 16296 = 291 × 56 16348 = 47 – 36 × 1 16375 = 47 – 9 × 16 16378 = -1 × 6 + (-3 + 7)7 (JD) 16383 = 26+8 – 13 16384 = (3 – 13)6+8 16385 = 86–4/3 + 1 (BH) 16387 = 86 / 16 + 3 16448 = 1 × 64 + 47 (BH) 16464 = 146–3 × 6 16480 = 47 + 96 × 1 16498 = 47 + 6 × 19 16524 = 51 × (3 × 6)2 16743 = 71+4 – 26 (BH) 16744 = 71+4 – 63 (BH) 16754 = 76–1 – 53 16758 = (1 + 6)5 – 7 × 7 16759 = 75 – 6 × 8 × 1 16765 = (74 – 6) × (6 + 1) 16790 = 76–1 – 8 – 9 16798 = 76 / 7 – 9 × 1 16799 = 76–19 – 8 16806 = -1 + (6 + 80)5 (BH) 16807 = (1 + 6)-80+6 (BH) 16808 = 76–1 + 80 16815 = (6 + 1)4+1 + 8 16816 = (6 + 1)5 + 8 + 1 16848 = 78 × 64–1 16854 = 5618 × 3 16855 = (6 + 1)5 + 48 16875 = 74+1 + 68 16876 = 1 + 68 + 75 16896 = (6 + 1)5 + 89 16976 = 169 + 75 17327 = 3 × 762 – 1 17328 = 3 × (77 – 1)2 17355 = 3471 × 5 17423 = (27 + 4)2 – 1 17424 = (27 + 4)3–1 17484 = 8 × (37 – 1) – 4 17488 = 8 × ((7 – 4)7 – 1) 17496 = 9 × (7 – 1)5 / 4 17508 = 75 + 701 17518 = 75 + 711 17528 = 75 + 721 17536 = 75 + 31+5 17537 = 1 + 75 + 36 (BH) 17538 = 75 + 731 17548 = 75 + 741 17558 = 75 + 751 17568 = 75 + 761 17578 = 75 + 771 17588 = 75 + 781 17598 = 75 + 791 17733 = 771 × 23 17857 = (8 × 56 – 1) / 7 18480 = 8 × (74 – 91) 18944 = (4 × 9 + 1) × 83 18954 = 81 × (35 – 9) 19321 = 1392 + 0 19322 = 1392 + 1 19323 = 1392 + 2 19324 = 1392 + 3 19325 = 1392 + 4 19326 = 1392 + 5 19327 = 1392 + 6 19328 = 1392 + 7 19329 = 1392 + 8 19330 = 1392 + 9 19428 = 9714×2 (JD) 19437 = 39–6×41 (JD) 19532 = 39–151 (JD) 19622 = (2+1)9–61 (JD) 19624 = 2–61+39 (JD) 19635 = (94–16)×3 (JD) 19638 = 9 × (37 – 6 + 1) 19647 = (4 – 1)9 – 62 19653 = (1 + 2)9 – 6 × 5 19654 = 39 – 6 × 5 + 1 19674 = 9 × (37 – 16) 19682 = -1 + (9 – 6)8+1 (JD) 19683 = (8 + 2 – 6 – 1)9 19684 = 1 + (9 – 6)8 × 3 (BH) 19685 = (4 – 1)9 + 8 – 6 19690 = (9 – 6)9 + 8 – 1 19692 = (6 / (1 + 1))9 + 9 19693 = (6 / 2)9 + 9 + 1 19732 = 39 + 71+1 19733 = 39 + 72 + 1 19734 = 17×3+39 (JD) 19737 = 1 × 9 × (37 + 6) 19739 = 39 + 7 × 8 × 1 19754 = 71+95/3 (JD) 19764 = 9 × ((6 + 7)3 – 1) 20460 = 4092×5 (JD) 20736 = (5 + 7)3+20 21895 = 1482–9 (JD) 22502 = 1502+2 (JD) 22540 = 92×(35+2) (JD) 22568 = 7×62×52 (JD) 22638 = 73 × (26 + 2) 22848 = 84×272 (JD) 23264 = 32×(36–2) (JD) 23330 = 93×32+2 (JD) 23326 = -2 + 3 × (3 × 2)5 23327 = (63+3 – 2) / 2 23328 = 3 × (2 × 3)7–2 23337 = 3 × (62+3 + 3) 23552 = 23×((5–1)5) (JD) 23646 = 563×42 (JD) 23716 = (157–3)2 (JD) 23763 = 2672/3 (JD) 23967 = 9×2663 (JD) 24334 = 2 × (-4 + 33)3 24392 = 294–1+3 (JD) 24456 = 24×(45–5) (JD) 24564 = 6 × ((3 + 5)4 – 2) 24510 = 4902×5 (JD) 24569 = 6 × 84 – 2 – 5 24570 = 945×26 (JD) 24576 = 2 × 45 × (7 + 5) 24582 = 482×51 (JD) 24624 = 64×(22–3) (JD) 24762 = 4127×6 (JD) 24948 = 92×7×44 (JD) 24960 = 4992×5 (JD) 24964 = (3 × 6 × 9 – 4)2 25600 = (9 × 5 + 5) × 29 25919 = 5 × (8 × 9)2 – 1 25920 = 5 × (9 × (9 – 1))2 26048 = 26×407 (JD) 26244 = 2 × 2 × (3 + 6)4 26248 = (27×6)2+4 (JD) 26250 = 2 × 2 × 94 + 6 26432 = 26×413 (JD) 26832 = 86×312 (JD) 26880 = 7 × (6 + 9) × 28 26984 = 8 × ((6 + 9)3 – 2) 27436 = 4 × (2 × 7 + 5)3 27644 = 27 × 63 – 4 27648 = 27 × 6-4+7 28188 = 182×87 (JD) 28222 = (8×21)2–2 (JD) 28224 = (83×2+2)2 (JD) 28476 = 28×(45–7) (JD) 28541 = (8+5)4–20 (JD) 28545 = (8 + 5)4 – 2 4 28550 = -2 + (8 + 5)4 – 9 28561 = (8 + 5)6–2 + 0 28562 = (8 + 5)6–2 + 1 28563 = 2 + (8 + 5)6–2 28564 = (8 + 5)6–2 + 3 28565 = (8 + 5)6–2 + 4 28566 = (8 + 5)6–2 + 5 28567 = (8 + 5)6–2 + 6 28568 = (8 + 5)6–2 + 7 28569 = (8 + 5)6–2 + 8 28570 = (8 + 5)6–2 + 9 28575 = (8 + 5)4 + 2 × 7 28672 = (2 / 8)-6 × 7 × 1 28675 = 7 × 84 + 6 / 2 28735 = 7 × (84 + 23) 28784 = 7 × 8 × (83 + 2) 28900 = (98+9×8)2 (JD) 29152 = 25×911 (JD) 29160 = 5 × (9 + 9)1+2 29275 = 2 × (2 + 9)4 – 7 29394 = (992–3)×3 (JD) 29397 = 992×3–6 (JD) 29518 = (95 + 1) / 2 – 7 29520 = 1 × (95 – 9) / 2 29522 = (95 – 1) / 2 – 2 29524 = (95 + 3) / 2 – 2 29525 = (2 × 95 + 2) / 4 (BH) 29526 = (95 + 5 – 2) / 2 (BH) 29528 = 95 / 2 + 7 / 2 (BH) 29530 = (95 + 9 + 2) / 2 (BH) 29548 = (47+95)/2 (JD) 29557 = (65+95)/2 (JD) 29575 = 7 × (5 × (4 + 9))2 31247 = 2 × (1 + 4)6 – 3 31250 = 2 × (1 + 4)9–3 31256 = 2 × (51+5 + 3) 31257 = 2 × (56 + 3) + 1 31347 = 36×1×43 (JD) 32699 = 83+2–69 (JD) 32735 = 47×2–33 (JD) 32742 = (47–13)×2 (JD) 32748 = 2 × (47 – 3 – 7) 32749 = 2 × (47 – 8) – 3 32755 = 2 × (47 – 5) – 3 32756 = 23+5 – 7 – 5 32758 = 2 × ((7 – 3)7 – 5) 32759 = 85–27/3 (JD) 32762 = 2 × (1 + 3)7 – 6 32765 = -3 + 27+6 × 4 (JD) 32768 = 6 / 3 × 27+7 32769 = 83+2 + 7 – 6 32774 = 2 × ((7 – 3)7 + 3) 32775 = (27 / 4)3 + 7 32785 = (38 – 4) × (7 – 2) 32795 = 2 × 47 + 3 × 9 32805 = 38 × (4 + 20) 32806 = 5 × 38 + 20 32840 = 323+9×8 (JD) 32815 = (38 + 2) × (4 + 1) 32816 = 5 × (38 + 2) + 1 32860 = 5 × (38 + 9 + 2) 33660 = 935×36 (JD) 33957 = 539×63 (JD) 34587 = 3 × (84 – 56) 34988 = (9 – 3)7 / 8 – 4 34992 = (9 + 9)4 / 3 × 1 35280 = 5 × (7 × (3 + 9))2 35715 = 7143×5 (JD) 35928 = (7 × 5 – 2)3 – 9 35937 = 3 × 9 × (5 + 6)3 36285 = 64×28–3 (JD) 36288 = 7 × (8 × (3 + 6))2 36450 = 93×(6+44) (JD) 36864 = (6 × 8)6–3 / 3 36945 = 34 + 9 × 46 37044 = (3 × 7)3 × 4 + 0 (JD) 37155 = 7431×5 (JD) 37175 = 37×17–4 (JD) 37206 = 702×53 (JD) 37230 = 73×(29–2) (JD) 37275 = 7×(732–4) (JD) 37688 = 8×7×673 (JD) 38413 = (2 × (8 – 1))4 – 3 38416 = (13 + 5 + 8)4 38417 = 13 + (6 + 8)4 38600 = 85 + (9 + 9)3 38637 = 38 × 6 – 36 39145 = 144+93 (JD) 39256 = (39–55)×2 (JD) 39270 = 39×2–96 (JD) 39276 = 2 × 9 × (37 – 5) 39279 = 39×2–87 (JD) 39286 = 2 × (39 – 5 × 8) 39288 = 39×2–78 (JD) 39295 = (4 × 9 – 2)3 – 9 39297 = 39×2–69 (JD) 39304 = (33+90)3 (JD) 39305 = 343+90 (JD) 39333 = 39×2–33 (JD) 39353 = 2 × (39 – 5) – 3 39356 = (39 – 5) × (5 – 3) 39357 = 6 × 33+5 – 9 39363 = 2 × 39 + 3 ‐ 6 39365 = 6 × 94 – 3 / 3 39366 = 39 × (3 – 6 + 5) 39369 = 6 × 38 + 9 / 3 39373 = 2 × (3 × 9)3 + 7 39382 = (39 + 8) × (3 – 1) 39384 = (38 + 3) × (9 – 3) 39393 = 3 × 9 + 39 × 2 39447 = 6 × 94 + 34 39525 = 93×425 (JD) 39618 = 93×71×6 (JD) 39627 = 629×63 (JD) 40860 = 908×45 (JD) 42999 = 29×84–9 (JD) 43218 = 74×(21–3) (JD) 43687 = (86 – 4) / 6 – 3 43690 = (89–3 – 4) / 6 43710 = 93×470 (JD) 43922 = 3 × (2 + 9)4 – 1 44064 = 64×34+0 (JD) 44370 = 34×(9+64) (JD) 44688 = 7448×6 (JD) 45210 = 9042×5 (JD) 45876 = (85×7+4)/5 (JD) 45892 = (94–5)×(8–1) (JD) 45924 = 94×(5+2)–3 (JD) 45927 = 94×(6×2–5) (JD) 45962 = (94+5)×(6+1) (JD) 45968 = (94+5)×7+6 (JD) 45983 = (94+8)×(5+2) (JD) 45988 = (94+8)×7+5 (JD) 46336 = 43×(36–5) (JD) 46468 = 66–47×4 (JD) 46577 = 66–75–4 (JD) 46612 = 66–4×11 (JD) 46613 = 66–42–1 (JD) 46614 = 1–43+66 (JD) 46620 = 66–9×4×1 (JD) 46624 = 2–34+66 (JD) 46626 = 64+2–6×5 (JD) 46630 = 66–(9+4)×2 (JD) 46636 = (6×6)3–5×4 (JD) 46640 = –4+66–3–9 (JD) 46644 = 4×(66/4–3) (JD) 46645 = 66–44/4 (JD) 46648 = 67/6–4–4 (JD) 46649 = 66+4/4–8 (JD) 46650 = 64×9×4–6 (JD) 46651 = –4+66–50 (JD) 46652 = -4 + 6 × 65 × 1 (BH) 46653 = 4+66–5–2 (JD) 46654 = -4 + 66 + 5 – 3 (BH) 46655 = 65×6–4/4 (JD) 46656 = 66+(5–5)×4 (JD) 46657 = 66+(6–5)4 (JD) 46658 = 4+66+5–7 (JD) 46659 = 66+5–8/4 (JD) 46661 = 4+66+60 (JD) 46662 = 6+6×64+1 (JD) 46663 = 4+66+6/2 (JD) 46664 = 66+6×4/3 (JD) 46666 = 4+6+6×65 (JD) 46673 = 24+66–7 (JD) 46676 = 67/6+5×4 (JD) 46684 = 4+66+8×3 (JD) 46688 = 67/6+8×4 (JD) 46692 = 66+9×4×1 (JD) 46698 = 49+66–7 (JD) 46737 = 34+67/6 (JD) 48028 = 8+74×20 (JD) 48060 = 89×540 (JD) 48746 = 54×78–4 (JD) 48750 = 78×(9–4)4 (JD) 49164 = (46+1)×(9+3) (JD) 49248 = 9×(742–4) (JD) 49392 = 143×(9+9) (JD) 49518 = 917×54 (JD) 50625 = (5×(0+6/2))4 (JD) 51249 = 54×82–1 (JD) 51250 = 54×(92+1) (JD) 51764 = 36×71+5 (JD) 52488 = 24×(8–5)7 (JD) 52493 = (9×2)4/2+5 (JD) 52499 = (94+2)×8–5 (JD) 53176 = 17×(55+3) (JD) 53248 = 45×(72+3) (JD) 53750 = 54×(93–7) (JD) 53824 = (35–8–3)2 (JD) 54368 = 65×7–43 (JD) 54427 = 64×42–5 (JD) 54428 = 7×(4+2)5–4 (JD) 54949 = 95–84–4 (JD) 55225 = (5×(5+42))2 (JD) 55290 = 95×582 (JD) 55790 = (58–95)/7 (JD) 55924 = –55+92+3 (JD) 55926 = 95+2–55 (JD) 56376 = 6×3×(7+55) (JD) 57493 = 54×92–7 (JD) 57500 = 54×(99–7) (JD) 57557 = 55+65×7 (JD) 58320 = 95–(8+1)3 (JD) 58424 = 38+2–54 (JD) 58914 = 9×(38–15) (JD) 58958 = 95–(8+5)×7 (JD) 58962 = 95–86–1 (JD) 58968 = 6–87+95 (JD) 58971 = 0–78+95 (JD) 58972 = 1–78+95 (JD) 58973 = 2–78+95 (JD) 58974 = 3–78+95 (JD) 58975 = 4–78+95 (JD) 58976 = 5–78+95 (JD) 58977 = 6–78+95 (JD) 58978 = 7–78+95 (JD) 58979 = 8–78+95 (JD) 58980 = 9–78+95 (JD) 58983 = 95–8×8–2 (JD) 58985 = 95–(8+8)×4 (JD) 58993 = 95+(2–9)×8 (JD) 58996 = 95–9×5–8 (JD) 59025 = 0–24+95 (JD) 59034 = (39–5+0)×3 (JD) 59040 = 95–9+3×0 (JD) 59043 = 95–4–2+0 (JD) 59044 = 95–4–30 (JD) 59045 = 95–4+4×0 (JD) 59046 = 95+50–4 (JD) 59047 = 95+4–6+0 (JD) 59048 = 95–740 (JD) 59049 = 84×0+95 (JD) 59050 = 940+95 (JD) 59053 = 20/5+95 (JD) 59054 = 95+5+3×0 (JD) 59055 = 95+5+40 (JD) 59063 = 20+95–6 (JD) 59130 = 95+92×1 (JD) 59184 = 9×(15+38) (JD) 59209 = 8×20+95 (JD) 59314 = 393–5×1 (JD) 59319 = 398–5×1 (JD) 59328 = 9+(7+25)3 (JD) 59334 = 393+5×3 (JD) 59400 = 9×39+95 (JD) 59454 = 95+34×5 (JD) 59535 = 35×49×5 (JD) 59569 = 8×65+95 (JD) 59625 = 95+(6×4)2 (JD) 59970 = 9995×6 (JD) 60416 = 45×(60–1) (JD) 60888 = 86×708 (JD) 62080 = 26×970 (JD) 62348 = 26×(74–3) (JD) 62416 = (56–21)×4 (JD) 62426 = 26×((5+2)4) (JD) 62428 = 74×26+2 (JD) 62452 = (56–12)×4 (JD) 62506 = 6+55×20 (JD) 62528 = 2×2×(7+56) (JD) 62694 = 36×(92–6) (JD) 63349 = 48–36×3 (JD) 63858 = 87×(36+5) (JD) 65440 = 45+3–96 (JD) 65479 = 86/4–57 (JD) 65480 = (9+7)4–56 (JD) 65481 = 5–60+48 (JD) 65485 = 48–6–45 (JD) 65490 = (9–5)8–46 (JD) 65524 = ((5+3)5–6)×2 (JD) 65529 = (85–6)×2+5 (JD) 65530 = 25×5–9–6 (JD) 65533 = 26+5+5–3 (JD) 65535 = 5+45+3–6 (JD) 65536 = (6–5–5)3+5 (JD) 65539 = (6–5–5)8+3 (JD) 65549 = 65/5+48 (JD) 65550 = (94–6)×(5+5) (JD) 65585 = 55+48–6 (JD) 65842 = 6×51+48 (JD) 66339 = 66+3×(38) (JD) 67226 = 75×(6–2)–2 (JD) 67228 = 76×2×2/7 (JD) 69888 = 896×78 (JD) 69957 = 9×(65+6–9) (JD) 69984 = 38×96/9 (JD) 70590 = 905×78 (JD) 72900 = ((9+9)×(8+7))2 (JD) 74364 = 37×34+6 (JD) 75433 = 47+35×2 (JD) 75625 = 2756–4 (JD) 75919 = (95+1–8)/7 (JD) 75920 = (95×9–1)/7 (JD) 75938 = 57–(9/3)7 (JD) 76723 = 2772–6 (JD) 76729 = 2778–6 (JD) 76825 = ((8+6)4)×2–7 (JD) 77553 = 57–572 (JD) 77579 = 57–78×7 (JD) 77936 = 57–9×7×3 (JD) 78057 = 0–68+57 (JD) 78114 = (8–3)7–11 (JD) 78116 = 57×1–8–1 (JD) 78117 = (11–6)7–8 (JD) 78123 = (8–2–1)7–2 (JD) 78124 = (8–3)7+1–2 (JD) 78125 = (8–12/4)7 (JD) 78126 = 182+57 (JD) 78127 = (6–18)7+2 (JD) 78133 = 8×1+(3+2)7 (JD) 78136 = 57×1+8+3 (JD) 78153 = 28+57×1 (JD) 78196 = 57+9×8–1 (JD) 78197 = 9×8+(6–1)7 (JD) 78253 = 57+82×2 (JD) 78453 = 82×4+57 (JD) 78573 = 57+82×7 (JD) 78984 = 9873×8 (JD) 79244 = (39+27)×4 (JD) 79507 = (50–7)9–6 (JD) 80100 = 9×8900 (JD) 81225 = (284+1)2 (JD) 81226 = 2852+1 (JD) 81648 = (8+1)×(64×7) (JD) 81696 = 96×851 (JD) 82944 = (9×32)8/4 (JD) 83491 = (9+8)4–30 (JD) 83494 = (9+8)4–33 (JD) 83755 = 35×(74–8) (JD) 85224 = 8×(5+223) (JD) 85293 = 92×2×(8+5) (JD) 85295 = 94×(8+5)+2 (JD) 86428 = 74×(62)–8 (JD) 87370 = (86–7)/3–9 (JD) 87379 = (87/8–7)/3 (JD) 87387 = 8+(86–7)/3 (JD) 91125 = (9×(4+1))2+1 (JD) 91126 = (9×5)2+1+1 (JD) 91136 = 11+(9×5)3 (JD) 91854 = 38×(19–5) (JD) 93025 = (309–4)2 (JD) 93657 = –93+6×56 (JD) 93696 = (59–3–9)×6 (JD) 93757 = 59–3×6+7 (JD) 94357 = 56+39×4 (JD) 94464 = 44×369 (JD) 97329 = 923/8–7 (JD) 97336 = (53–7)9/3 (JD) 98316 = 9+(85+1)×3 (JD) 98355 = (39–8–4)×5 (JD) 98415 = 184–94 (JD) 98475 = (94+4)×(8+7) (JD) 98535 = 5×3×(94+8) (JD) 99225 = (9–92×4)2 (JD)

Almost Friedman Numbers (written with the digits of n+1)
 1225 = (62 – 1)2 1262 = 631 × 2 (JD) 1278 = 71 × 9 × 2 (JD) 1331 = (13 – 2)3 (JD) 1333 = 43 × 31 (JD) 1353 = 451 × 3 (JD) 1372 = (1 + 3) × 73 1373 = 4 × 73 + 1 1525 = 61 × 25 (JD) 1542 = 514 × 3 (JD) 1555 = (65 – 1) / 5 1626 = 271 × 6 (JD) 1638 = 91 × 6 × 3 (JD) 1911 = 91 × 21 (JD) 1935 = (63 – 1) × 9 2048 = 29 × 4 + 0 2136 = 712 × 3 (JD) 2176 = 17 × 27 (JD) 2178 = (2 + 1)7 – 9 2196 = (2 + 1)7 + 9 2336 = 73 × 32 (JD) 2500 = 502 × 1 2548 = 52 × 49 (JD) 2688 = 96 × 28 (JD) 2784 = 87 × 25 (JD) 2912 = 91 × 32 (JD) 2915 = (9 × 6)2 – 1 2916 = (9 × (7 – 1))2 3124 = (3 + 2)5 – 1 3125 = (3 + 2)6–1 3155 = 631 × 5 (JD) 3277 = (38 – 7) / 2 3280 = (38 – 1) / 2 3282 = (38 + 3) / 2 3375 = (3 × 7 – 6)3 3478 = 94 × 37 (JD) 3600 = 603–1 (JD) 3650 = (36 + 1) × 5 3724 = 532 × 7 (JD) 3748 = 937 × 4 (JD) 3773 = 73 × (4 + 7) 3853 = 84 – 35 3913 = 91 × 43 (JD) 4095 = 46 – 90 4096 = (7 + 90)4 4097 = 84 + 90 4672 = 73 × 64 (JD) 4914 = 91 × 54 (JD) 5185 = 85 × 61 (JD) 5471 = 742 – 5 (JD) 5476 = 747–5 (JD) 5832 = 35 × 3 × 8 5915 = 91 × 65 (JD) 6144 = 6 × 1 × 45 6188 = 91 × 68 (JD) 6250 = (6 – 1)5 × 2 6495 = 94 – 66 (JD) 6666 = (66 + 6) / 7 6748 = 964 × 7 (JD) 6916 = 91 × 76 (JD) 7917 = 91 × 87 (JD) 8918 = 98 × 91 (JD) 9215 = 962 – 1 (JD) 9216 = (97 – 1)2 (JD) 10570 = 151 × 70 10860 = 60 × 181 10920 = 12 × 910 11024 = 1052 – 1 11025 = (106 – 1)2 11236 = (113 – 7)2 11264 = 11 × (-2 + 6)5 11628 = 612 × 19 11663 = -1 + 1 × 66 / 4 11664 = 1 × 66 / (5 – 1) 11767 = 1681 × 7 11934 = 9 × (113 – 5) 11972 = 9 × 113 – 7 12062 = 6031 × 2 12100 = 1 × 1102 12288 = 192 × 82 12348 = 9 × 143 / 2 12393 = (24 + 1) × 93 12444 = 244 × 51 12466 = 271 × 46 (JD) 12488 = 892 × 14 12505 = 205 × 61 12544 = 4 × (55 + 1)2 12545 = 4 × 562 + 1 12586 = 217 × 58 12597 = (28 – 9) × 51 12602 = 6301 × 2 12638 = 6319 × 2 12768 = 672 × 19 12800 = (1 + 1) × 802 12801 = 1 + 2 × 802 12816 = 712 × 18 12874 = 157 × 82 12978 = 721 × (9 + 9) 13122 = 1 × 2 × 323 13224 = (23 × 5)2 – 1 13225 = (23 × (6 – 1))2 13286 = 73 × 182 13377 = (31 + 8) × 73 13378 = 39 × 73 + 1 13503 = 4501 × 3 13671 = 217 × 63 (BH) 13797 = 891 × 73 13822 = (3 × 8)3 – 1 × 2 13823 = (2 × (4 + 8))3 – 1 13824 = 1 × (3 × 8)-2+5 13825 = (6 × 8 / 2)3 + 1 13855 = 163 × 85 13924 = (59 × (3 – 1))2 13946 = 734 × 19 13965 = 19 × (36 + 6) 14194 = 151 × 94 14375 = 6 × 74 – 31 14406 = (10 – 4) × 74 14640 = (1 + 4 + 6)4 – 1 14641 = (2 + 4 + 6 – 1)4 14644 = (5 + 6)4 + 4 – 1 14645 = (6 + 6 – 1)4 + 4 14646 = (4 + 7)4 + 6 – 1 14647 = (4 + 8 – 1)4 + 6 14758 = (95 – 17) / 4 14872 = 3714 × 4 14896 = 784 × 19 15025 = 601 × 25 15042 = 5014 × 3 15305 = 3061 × 5 15325 = 613 × 25 15386 = 7 × ((5 + 8)3 + 1) 15435 = (6 + 1)3 × 45 15436 = 73 × 45 + 1 15525 = 621 × 5 × 5 15552 = (1 + 5)5 × (5 – 3) 15561 = (65 + 5) × 2 – 1 15562 = (65 + 5) × (3 – 1) 15564 = 5 × 56 – 61 15567 = 56 – 58 × 1 15572 = 57–1 – 53 15574 = 57 / 5 – 51 15576 = 51+5 – 7 × 7 15584 = -1 + (55 – 8) × 5 15585 = 56 – 5 × 8 × 1 15607 = 56 – 18 + 0 15612 = 1 × 56 – 13 15616 = -1 + 56 – 1 – 7 15617 = 1 × 56 – 1 × 8 15618 = 1 + 56 – 1 + 9 15621 = 1 × 56 – 2 – 2 15622 = 56 – 3 × 12 15623 = 1 × 56 + 2 – 4 15624 = 56 – 125 15625 = (15 / 6 × 2)6 (JD) 15626 = 56 + 127 15627 = 56 + 2 × 18 15628 = 56 + 2 + 19 15629 = 1 + 56 + 3 + 0 15630 = 1 + 56 + 3 + 1 15631 = 1 + 56 + 3 + 2 15632 = 1 + 56 + 3 + 3 15633 = 1 + 56 + 3 + 4 15634 = 1 + 56 + 3 + 5 15635 = 1 + 56 + 3 + 6 15636 = 1 + 56 + 3 + 7 15637 = 1 + 56 + 3 + 8 15638 = 1 + 56 + 3 + 9 15639 = 56 + 14 + 0 15640 = 56 + 14 + 1 15641 = 1 × 56 + 42 (JD) 15642 = 56 + 14 + 3 15643 = 56 + 14 + 4 15644 = -1 + 56 + 4 × 5 (JD) 15645 = 56 + 14 + 6 15646 = 56 + 14 + 7 15647 = 56 + 14 + 8 15648 = 56 + 14 + 9 15650 = 56 + 51+1 15651 = 1 + 56 + 52 15654 = -1 + 5 × (6 + 55) 15655 = 1 × 5 × 6 + 56 15657 = 56 + 8 × (5 – 1) 15661 = 1 × 56 + 62 15662 = 56 + 36 + 1 15666 = 56 + 6 × 7 – 1 15667 = 56 + 6 × (8 – 1) 15673 = 56 + 47 + 1 15683 = (1 + 4)6 + 58 15684 = 56 + 58 + 1 15688 = 56 + 9 × (8 – 1) 15694 = 51+5 + 69 15695 = 56 + 69 + 1 15697 = 1 × 56 + 9 × 8 15762 = 56 + 137 15793 = 47 – 591 15805 = 56 + 180 15871 = (18 × 7)2 – 5 15872 = (5 – 1)7 – 83 15876 = (18 × 7)7–5 15906 = 75 – 901 16206 = 2701 × 6 16224 = 522 × 6 × 1 16348 = (46 – 9) × (1 + 3) 16354 = 56 + 31+5 16355 = 56 + 36 + 1 16356 = 56 + 731 16371 = (6 – 2)7 – 13 16377 = (3 – 1)6+8 – 7 16378 = (1 + 9 / 3)7 – 6 16381 = 26+8 – 3 × 1 16383 = 86 – 4/3 – 1 16384 = 1 / 6 × 3 × 85 16385 = 1 + (6 / 3)8+6 (JD) 16386 = (1 + 3)7 + 8 – 6 16393 = 46 × (1 + 3) + 9 16397 = 863 × 19 16426 = 214 + 6 × 7 16434 = (143 – 5) × 6 16444 = (46 + 15) × 4 16445 = 4 × 46 + 61 16474 = 47 + 6 × 15 16525 = 661 × 25 16538 = 56 + 913 16596 = 56 + 971 16632 = 33 × 616 16734 = (1 + 6)5 – 73 16743 = 71+4 – 26 16744 = 75 – 64 + 1 16746 = 7 × 74 – 61 16753 = 76–1 – 54 16756 = 76 / 7 – 51 16794 = 75 – 19 + 6 16798 = 76 – 19 – 9 16806 = 76–1 – 80 16807 = (8 – 80)6–1 16813 = (8 – 1)4+1 + 6 16814 = 1 + 6 + (8 – 1)5 16815 = (6 + 1)6–1 + 8 16816 = 76–1 + 8 + 1 16853 = (8 – 1)5 + 46 16855 = (6 + 1)5 + 6 × 8 16856 = 75 + 6 × 8 + 1 16871 = 76–1 + 82 16874 = -1 + 68 + 75 16875 = 76–1 + 68 16896 = 76–1 + 89 17325 = 3 × (762 – 1) 17424 = 4 × (71 – 5)2 17482 = 8 × 37 – 14 17492 = (9 – 1) × 37 – 4 17496 = (9 – 1) × (7 – 4)7 17500 = 7 × 501+1 17501 = 1 + 7 × 502 (JD) 17535 = -1 + 75 + 36 17536 = (1 + 7) × (5 + 37) 17537 = 8 × (5 + 37) + 1 17649 = 105 – 76 17848 = 184 × 97 17952 = (73 + 9) × 51 17993 = 947 × 19 18225 = (2 × 68 – 1)2 18414 = 18 × (45 – 1) 18450 = 18 × (45 + 1) 18538 = 598 × 31 18662 = 86 × (63 + 1) 19262 = 9631 × 2 19320 = (139 – 1)2 19342 = 39 – 341 19386 = 718 × 9 × 3 19427 = (4 – 1)9 – 28 19531 = 39–152 (JD) 19592 = 95/3–91 (JD) 19621 = (2+1)9–62 (JD) 19622 = 1–62+39 (JD) 19638 = 39 – 9 × (6 – 1) 19642 = (6–3)9–41 (JD) 19652 = 39 – 6 × 5 – 1 19653 = (4 – 1)9 – 6 × 5 19662 = 63×91+6 (JD) 19672 = 6–17+39 (JD) 19681 = (8 + 1 – 6)9 – 2 19682 = -1 + (9 – 6)8 × 3 (BH) 19683 = (4 – 16+8)9 19684 = (5 + 6 – 8)9 + 1 19691 = (6 / 2)9 + 9 – 1 19692 = 39 + 9 × 16 19725 = (1 + 2)9 + 6 × 7 19731 = 39 + 72 – 1 19732 = 39 + 73–1 19734 = 51+37×9 (JD) 19746 = 9 × ((4 – 1)7 + 7) 20480 = 84×10/2 (JD) 20482 = 83×40+2 (JD) 20488 = 29×40+8 (JD) 20930 = 91×230 (JD) 21036 = 7012×3 (JD) 21248 = 124+29 (JD) 21266 = 62×(72+1) (JD) 21306 = 7102×3 (JD) 21316 = (73×2)1+1 (JD) 21424 = 52×412 (JD) 21845 = 2 × (48 – 1) / 6 21853 = 412×(8+5) (JD) 21952 = (2 × 1 × (9 + 5))3 22050 = 1052×2 (JD) 22344 = 532×42 (JD) 22358 = 35×92+2 (JD) 22386 = 82×273 (JD) 22448 = 92×244 (JD) 22500 = (50×(2+1))2 (JD) 22502 = (5×30)2+2 (JD) 22842 = 34×282 (JD) 22878 = 279×82 (JD) 22898 = ((99+8)2)×2 (JD) 23264 = 25 × (36 – 2) 23325 = 62×3 / 2 – 3 23328 = 22+3 × 93 23334 = 3 × (2 + (3 + 3)5) 23355 = 3 × (32 + 65) 23360 = 32×(36+1) (JD) 23716 = (7 × (3 × 7 + 1))2 23808 = 28×93+0 (JD) 23828 = 92×(28+3) (JD) 23872 = 82×373 (JD) 23884 = 853×28 (JD) 23976 = 9×72×37 (JD) 23987 = 289×83 (JD) 24025 = (620/4)2 (JD) 24334 = 2 × (4 × 5 + 3)3 24378 = 293–7–4 (JD) 24389 = 294×0+3 (JD) 24390 = 293+14 (JD) 24391 = 293+4–2 (JD) 24576 = 24+7 × (5 + 7) 24582 = (2 + 45 × 8) × 3 (BH) 24628 = 94×262 (JD) 24668 = 92+46×6 (JD) 24744 = 24×(7+45) (JD) 24856 = 478×52 (JD) 24984 = 8 × (59–4 – 2) 25000 = 502×10 (JD) 25175 = (712–6)×5 (JD) 25196 = 712×5–9 (JD) 25281 = (82×2–5)2 (JD) 25313 = (1 + (3 × 5)4) / 2 25375 = 7×3625 (JD) 25392 = (925–3)×3 (JD) 25591 = (5 × 25)2 – 9 25830 = 82×315 (JD) 25932 = (932–5)×3 (JD) 25948 = 499×52 (JD) 26172 = 12×(37–6) (JD) 26240 = 1622–4 (JD) 26242 = 4 × 32+6 – 2 26244 = 4 × (5 – 2)2+6 26316 = 62×731 (JD) 26488 = 946×28 (JD) 26624 = 26×((6–2)5) (JD) 26752 = 76×352 (JD) 26782 = 3826×7 (JD) 26892 = 62×9×83 (JD) 26971 = (9+622)×7 (JD) 27188 = 971×28 (JD) 27388 = 82×(73–9) (JD) 27520 = 27×215 (JD) 27648 = 27 × 6 × 4 × 9 27783 = ((28–7)4)/7 (JD) 27790 = 7 × ((7 × 9)2 + 1) 27848 = 8 × (7 × 9 – 4)2 28126 = 82×(72+1) (JD) 28224 = (85×2–2)2 (JD) 28372 = 82×(73+3) (JD) 28512 = 81×352 (JD) 28536 = 82×(73+5) (JD) 28540 = (8+5)4–21 (JD) 28560 = (8 + 5)6–2 – 1 28561 = (2 + 5 + 6)8/2 28566 = (6 + 7)8/2 + 5 28567 = (8 + 5)8/2 + 6 28646 = 84×7–26 (JD) 28666 = 7 × (8 / 2)6 – 6 28672 = 7 × 83 × (2 + 6) 28678 = 7 × 8 × 29 + 6 28782 = 82×(8+73) (JD) 28900 = (10×(9+8))2 (JD) 29136 = 9712×3 (JD) 29184 = 29×(58–1) (JD) 29241 = (2 + (9 + 4)2)2 29396 = 992×3–7 (JD) 29512 = 952×31 (JD) 29516 = (95–17)/2 (JD) 29517 = (95 + 1) / 2 – 8 29522 = (95 – 2 – 3) / 2 29524 = (95 – 5) / 2 + 2 29526 = (95 + 7) / 2 – 2(BH) 29528 = (95 + 9 – 2) / 2 (BH) 29532 = 3 × (39 + 5) / 2 29538 = (95 + 3 × 9) / 2 (BH) 29550 = (51+95)/2 (JD) 29566 = 652×7–9 (JD) 29575 = ((9+56)2)×7 (JD) 29696 = 29×(67–9) (JD) 29743 = 4249×7 (JD) 30155 = 6031×5 (JD) 30515 = 6103×5 (JD) 30650 = 613×50 (JD) 30878 = 73×90+8 (JD) 30940 = 91×340 (JD) 31250 = (1 + 1) × 52×3 31251 = 2 × 52×3 + 1 31252 = 2 × (53+3 + 1) 31255 = 2 × (56 + 3) – 1 31256 = 2 × (57–1 + 3) 31347 = 43×((8+1)3) (JD) 31348 = 93×43+1 (JD) 31505 = 6301×5 (JD) 31595 = 6319×5 (JD) 31688 = 3961×8 (JD) 31955 = 6391×5 (JD) 32500 = 502×13 (JD) 32682 = 323–86 (JD) 32740 = (213–7)×4 (JD) 32747 = 48 / 2 – 3 × 7 32753 = 2 × 47 – 3 × 5 32754 = (3 + 5)5 – 2 × 7 32755 = 23+5 – 6 – 7 32757 = 85 + 3 – 2 × 7 32761 = 26×2+3 – 7 32764 = (2 + 6)5 – 7 + 3 32767 = 82+3 – 7 + 6 32768 = (-3 – 2 + 7)6+9 32770 = 2 × ((7 – 3)7 + 1) 32771 = 3 + 27+7 × 2 (BH) 32775 = 23×7–6 + 7 32784 = 32 + 7 + 85 32804 = 5 × 38 – 20 32805 = 38 × (6 – 20) 32814 = 5 × (38 + 2) – 1 32815 = (38 + 2) × (6 – 1) 32834 = 33×2+85 (JD) 32835 = (38 + 6) × (3 + 2) 33497 = 93 + (4 × 8)3 33750 = 153×(7+3) (JD) 34591 = 932×4–5 (JD) 34596 = (937–5)×4 (JD) 34816 = 83×17×4 (JD) 34856 = 8×4357 (JD) 34911 = 92×431 (JD) 34965 = 3 × (66 / 4 – 9) 34968 = 6 × ((9 + 9)3 – 4) 34986 = 73×(98+4) (JD) 34992 = 3 × 9 × (9 – 3)4 35280 = ((83+1)2)×5 (JD) 35283 = 842×5+3 (JD) 35478 = 9×73×54 (JD) 35721 = (7 × (5 – 2)3)2 35840 = 83×5×14 (JD) 35932 = 339/3–5 (JD) 35937 = 339/(8–5) (JD) 35942 = (9 × 4 – 3)3 + 5 35946 = (7 × 4 + 5)3 + 9 36288 = 82×9×63 (JD) 36478 = 793×46 (JD) 36500 = 50×(36+1) (JD) 36648 = 9 × 46 – 63 36862 = ((6 × 8)3 – 6) / 3 36891 = 9 × ((8 / 2)6 + 3) (BH) 36945 = (3 + 6) × (9 + 46) 36947 = 83+46×9 (JD) 36948 = 3 + 9 × (9 + 46) 37084 = 508×73 (JD) 37174 = 37×17–5 (JD) 37324 = 7×5332 (JD) 37348 = 9337×4 (JD) 37468 = 9367×4 (JD) 37492 = 9373×4 (JD) 37543 = 75 + (3 × 4)4 37555 = 7×5365 (JD) 37814 = 518×73 (JD) 38298 = 982×39 (JD) 38413 = 148–4–3 (JD) 38415 = (6 + 8)4 – 13 38416 = 8 × (3 – 1) × 74 38424 = (5 + 32)4 + 8 38425 = (6 + 8)4 + 32 38428 = (982+3)×4 (JD) 38440 = 144+8×3 (JD) 39285 = 6 × 38 – 92 39303 = 343–90 (JD) 39304 = (39–5)3+0 (JD) 39313 = 9+343×1 (JD) 39323 = 39×2–43 (JD) 39345 = 6 × (94 – 3) – 3 39348 = (94 – 3) × (9 – 3) 39351 = 2 × 39 – 3 × 5 39360 = 39 × (3 – 1) – 6 39363 = 39 × (6 – 4) – 3 39366 = 39 × (3 + 6 – 7) 39373 = 2 × 3 × 94 + 7 39375 = 3 × 6 × 37 + 9 39744 = 54×(93+7) (JD) 39748 = 9937×4 (JD) 40590 = 9×4510 (JD) 40880 = 10×(84–8) (JD) 40950 = 91×450 (JD) 40960 = (9 + 1) × 46 + 0 41391 = 34 × (29 – 1) 41664 = 64×651 (JD) 41971 = 472×19 (JD) 42588 = 84×(29–5) (JD) 42592 = ((49–5)3)/2 (JD) 42688 = 928×46 (JD) 43264 = (52×4)6/3 (JD) 43681 = (836/4)2 (JD) 43685 = (86–34)/6 (JD) 43688 = 49 / 6 – 8 /3 43690 = (49 – 1 – 3) / 6 43693 = (49 – 4) / 6 + 3 43697 = (38+49)/6 (JD) 43740 = 4 × 37 × (4 + 1) 43744 = 4 + 37 × 4 × 5 43752 = 4 × (37 × 5 + 3) 43764 = 4 × (37 × 5 + 6) 43784 = 8×5473 (JD) 43920 = 3 × ((9 + 2)4 – 1) 43921 = 3 × (9 + 2)4 – 2 43923 = 3 × (9 – 2 + 4)4 45355 = 64×35–5 (JD) 45357 = 54+3–85 (JD) 45360 = 64×1×35 (JD) 45375 = (64×7+3)×5 (JD) 45535 = 35×(64+5) (JD) 45632 = –(45–63+3) (JD) 45635 = 66+3–45 (JD) 45760 = 715×64 (JD) 45872 = 8×5734 (JD) 45920 = (94–1)×(5+2) (JD) 45923 = 94×(5+2)–4 (JD) 45927 = (98–4)×(5+2) (JD) 46272 = 723×64 (JD) 46315 = 66–341 (JD) 46531 = 64+2–53 (JD) 46535 = 66+4–53 (JD) 46567 = 66–85–4 (JD) 46612 = 66–43–1 (JD) 46613 = 1–44+66 (JD) 46620 = 62×(64–1) (JD) 46624 = 66–45/2 (JD) 46626 = 66–7×4–2 (JD) 46628 = 66+(2–9)×4 (JD) 46632 = –(4×6–63+3) (JD) 46634 = 6×(65–3)–4 (JD) 46635 = 66+3–6×4 (JD) 46638 = (69–4–3)×6 (JD) 46640 = 66–4×4×1 (JD) 46647 = 66–8–4/4 (JD) 46648 = 66+4/4–9 (JD) 46650 = 66–5–14 (JD) 46651 = (64/6)2–5 (JD) 46652 = 4 + 66 – 5 – 3 (BH) 46653 = –4+66+5–4 (JD) 46655 = 66–(6–5)4 (JD) 46656 = 6(7+5)/6+4 (JD) 46657 = 4+66+5–8 (JD) 46659 = 4+66–60 (JD) 46660 = 4+6×(66–1) (JD) 46661 = 66+(6+4)/2 (JD) 46662 = 4+66+6/3 (JD) 46663 = 66+6+4/4 (JD) 46665 = 66+6×6/4 (JD) 46666 = 67/6+6+4 (JD) 46668 = 66+(9–6)×4 (JD) 46670 = 14+67/6 (JD) 46671 = 66+7+4×2 (JD) 46672 = 66+(7–3)×4 (JD) 46674 = (65+7–4)×6 (JD) 46675 = 76/4+66 (JD) 46680 = 66+8×(4–1) (JD) 46682 = 34+66–8 (JD) 46684 = 66+8+5×4 (JD) 46692 = (9×4)3+6×6 (JD) 46697 = 49+66–8 (JD) 46728 = 649×72 (JD) 46734 = (56–47)×3 (JD) 46962 = 9×34+66 (JD) 47524 = (7–5×45)2 (JD) 47688 = 7948×6 (JD) 48020 = 20×((8–1)4) (JD) 48128 = 94×(82+1) (JD) 48256 = 82×754 (JD) 48692 = 94×(83+6) (JD) 48750 = 54×1×78 (JD) 48762 = 34×86×7 (JD) 48841 = (4/884)–2 (JD) 48936 = (47–9×8)×3 (JD) 49152 = 49/(5+1/3) (JD) 49161 = 9+46×12 (JD) 49164 = 964×51 (JD) 49260 = 12×(9+46) (JD) 50960 = 91×560 (JD) 51085 = 85×601 (JD) 51688 = 91×568 (JD) 51845 = (64×8+1)×5 (JD) 52020 = 512×20 (JD) 52136 = 73×152 (JD) 52428 = (49–2+2)/5 (JD) 52448 = 4×2×(94–5) (JD) 52480 = 28×5×41 (JD) 52488 = 94×(28–5) (JD) 52493 = 5+2×4×(94) (JD) 52896 = 928×57 (JD) 53183 = 13×(84–5) (JD) 53361 = (63+5×3)2 (JD) 53488 = (94+53)×8 (JD) 54272 = 53×(47–2) (JD) 54375 = 75×(36–4) (JD) 54868 = 946×58 (JD) 54872 = (85–47)3 (JD) 54925 = 652×(9+4) (JD) 54953 = 95–45×4 (JD) 55296 = 2/9×((7+5)5) (JD) 56185 = 85×661 (JD) 56250 = 55×(6+12) (JD) 56252 = 55×6×3+2 (JD) 56490 = 9415×6 (JD) 56862 = 36×6×(8+5) (JD) 57344 = 45×7×(5+3) (JD) 57347 = 45×8×7+3 (JD) 57848 = 8×7×(9+45) (JD) 58178 = 95–871 (JD) 58320 = 183×5×2 (JD) 58921 = 95–82×2 (JD) 58961 = 95–86–2 (JD) 58965 = 95–(8+6)×6 (JD) 58967 = 6–88+95 (JD) 58968 = 95–98–6 (JD) 58970 = 95–8–71 (JD) 58972 = 95–(8+3)×7 (JD) 58974 = 95–(8+7)×5 (JD) 58978 = 8–79+95 (JD) 58982 = 95–8×8–3 (JD) 58984 = (85×9+8)/5 (JD) 58985 = 95–88–6 (JD) 58986 = 9×((8–5)8–7) (JD) 59024 = 0–25+95 (JD) 59034 = 95–5×3+0 (JD) 59041 = 95–4×2+0 (JD) 59042 = 95–4–3+0 (JD) 59044 = –(5–90×4+5) (JD) 59045 = 96×0+5–4 (JD) 59046 = 95+4–7+0 (JD) 59047 = 95–8/4+0 (JD) 59048 = 95–940 (JD) 59049 = 50×0+95 (JD) 59050 = 95+5×0+1 (JD) 59051 = 95+5×0+2 (JD) 59052 = 95+5×0+3 (JD) 59053 = 95+5×0+4 (JD) 59054 = 5+90×5+5 (JD) 59055 = 95+6+5×0 (JD) 59056 = 95+7+5×0 (JD) 59057 = 95+8+5×0 (JD) 59058 = 9+95+5×0 (JD) 59061 = 6×2+95+0 (JD) 59072 = 30+95–7 (JD) 59094 = 5×9+0+95 (JD) 59115 = 6×11+95 (JD) 59151 = 51×2+95 (JD) 59217 = 8×21+95 (JD) 59235 = 62×3+95 (JD) 59265 = 95+66/2 (JD) 59292 = 95+92×3 (JD) 59319 = 395–2+0 (JD) 59320 = 395–2+1 (JD) 59321 = 395–2+2 (JD) 59322 = 395–2+3 (JD) 59323 = 395–2+4 (JD) 59324 = 395–2+5 (JD) 59325 = 395–2+6 (JD) 59326 = 395–2+7 (JD) 59327 = 395–2+8 (JD) 59328 = 9+395–2 (JD) 59364 = 63×5+95 (JD) 59418 = 9×41+95 (JD) 59535 = (39–65)×5 (JD) 59625 = 9×6625 (JD) 59685 = 69×865 (JD) 60970 = 91×670 (JD) 61236 = 36×7×12 (JD) 61440 = 46×(4+11) (JD) 61444 = 46×15+4 (JD) 61838 = 98×631 (JD) 62184 = 8×(65–2–1) (JD) 62298 = 9×6922 (JD) 62464 = 56×4–62 (JD) 62472 = ((3+2)6–7)×4 (JD) 62474 = (56–7)×4+2 (JD) 62484 = 56×4–8×2 (JD) 62500 = 20×(56–1) (JD) 62644 = (62+56)×4 (JD) 62784 = 8×(72+65) (JD) 62848 = 982×64 (JD) 63488 = 84×93/6 (JD) 64512 = 45×1×63 (JD) 64917 = 48–619 (JD) 65480 = 5–61+48 (JD) 65491 = 46+2–9×5 (JD) 65497 = 48–9–6×5 (JD) 65511 = 216–5×5 (JD) 65530 = (5–1)5+3–6 (JD) 65531 = (6–2)5+3–5 (JD) 65533 = (6+5+5)4–3 (JD) 65536 = (6+5+5)–3+7 (JD) 65541 = 46/2+5+5 (JD) 67228 = ((96+2)2)×7 (JD) 67244 = (75+6–2)×4 (JD) 67256 = (7+75)×(6–2) (JD) 67438 = 9634×7 (JD) 67648 = 9664×7 (JD) 68121 = (28+6–1)2 (JD) 68913 = 419–6–8 (JD) 68921 = (82/2)9–6 (JD) 68975 = 68/9–76 (JD) 69216 = 96×721 (JD) 69255 = (6/2)6×95 (JD) 69350 = 95×(36+1) (JD) 69547 = (46–5)×(9+8) (JD) 69616 = 916×76 (JD) 69748 = 9964×7 (JD) 69984 = 96×98–5 (JD) 69993 = 9+9×69–4 (JD) 70980 = 91×780 (JD) 72030 = 73×210 (JD) 73728 = (7–3)7/2×9 (JD) 73751 = 57–37×2 (JD) 74888 = 8/7×(48–9) (JD) 74897 = (48×8–9)/7 (JD) 75915 = (96–1)/7–5 (JD) 75938 = 57–39/9 (JD) 76832 = 73×(8+63) (JD) 77284 = 2787–5 (JD) 77552 = 57–573 (JD) 77656 = 57–7×67 (JD) 77657 = 57–78×6 (JD) 78122 = (8–3)7–2–1 (JD) 78123 = (8+1–4)7–2 (JD) 78124 = 57–182 (JD) 78125 = (18/6+2)7 (JD) 78126 = 18+(7–2)7 (JD) 78133 = 8+(4+13)7 (JD) 78134 = 57+8+13 (JD) 78141 = 8×2+(4+1)7 (JD) 78152 = 81/3+57 (JD) 78153 = 7×4+58–1 (JD) 78174 = 7×7+58–1 (JD) 78253 = 57+42×8 (JD) 78381 = 28+(8–3)7 (JD) 78555 = 86×5+57 (JD) 79233 = 74×3×(9+2) (JD) 79831 = 97×823 (JD) 80990 = 91×890 (JD) 80992 = 903/9–8 (JD) 81224 = 2852–1 (JD) 81225 = (286–1)2 (JD) 81648 = (8–1)×(64×9) (JD) 82488 = 982×84 (JD) 82935 = (8×36)2–9 (JD) 82944 = ((9–45)×8)2 (JD) 83200 = 802×13 (JD) 83490 = (9+8)4–31 (JD) 83497 = (9+8)4–8×3 (JD) 83513 = –8+(3/51)–4 (JD) 83518 = (9+8)5–1–3 (JD) 83521 = (5×3+2)8/2 (JD) 83678 = 973×86 (JD) 84672 = (846–3)/7 (JD) 84778 = 97×874 (JD) 85192 = (9×5–1)3+8 (JD) 85293 = ((5–2)8)×(9+4) (JD) 86272 = 28×(73–6) (JD) 86428 = (49×6)2–8 (JD) 86436 = 36×(78–4) (JD) 87500 = 105×7/8 (JD) 87536 = 8×(7+5×(37)) (JD) 87622 = (8×37)2+6 (JD) 90250 = 952×10 (JD) 91124 = (9×5)2+1–1 (JD) 91125 = (9×(6–1))2+1 (JD) 93750 = (59–3)×(7–1) (JD) 97336 = (7×7–9/3)3 (JD) 97345 = 9+(7×6+4)3 (JD) 98034 = (85–90)×3 (JD) 98304 = 85×3+9×0 (JD) 98313 = 9+(84+1)×3 (JD) 98314 = 85×3+9+1 (JD) 98331 = (9+83+2)×3 (JD) 98334 = (9+85)×3+3 (JD) 98351 = 39×5–82 (JD) 98353 = 49+85×3 (JD) 98358 = (85+9+9)×3 (JD) 98415 = 94×(8+6+1) (JD) 98416 = 94×(8+7)+1 (JD) 99225 = (9×(9+26))2 (JD) 99234 = 9+(9×35)2 (JD)

An integer n is called an non-integral Friedman number if, using the digits of n, the four basic arithmetic operations, exponentiation, and parentheses, we can create an expression which evaluates to a non-integer within 1 of n. Here are the known non-integral Friedman numbers with 5 or fewer digits.

Non-Integral Friedman Numbers (rounding down)
 1364 ≈ 46 / 3 – 1 1365 ≈ (5 – 1)6 / 3 1448 ≈ 814/4 1555 ≈ (1 + 5)5 / 5 1556 ≈ 65 / 5 + 1 1562 ≈ (6 – 1)5 / 2 1674 ≈ 64 + 1/7 1845 ≈ (18 / 4)5 3280 ≈ 38 / 2 + 0 3281 ≈ 38 / 2 + 1 3282 ≈ 38 / 2 + 2 3283 ≈ 38 / 2 + 3 3284 ≈ 38 / 2 + 4 3285 ≈ 38 / 2 + 5 3286 ≈ 38 / 2 + 6 3287 ≈ 38 / 2 + 7 3288 ≈ 38 / 2 + 8 3289 ≈ 38 / 2 + 9 3544 ≈ (3 / 5)-4×4 (JD) 4328 ≈ (8 + 3-2)4 (JD) 6285 ≈ (6 – 2/8)5 6997 ≈ 967/9 7498 ≈ 8 × 94 / 7 7985 ≈ 89 / 75 (JD) 10697 ≈ 1067/9 11663 ≈ (66 – 1) / (3 + 1) 11664 ≈ (1+1+66)/4 (JD) 12467 ≈ 4761/2 12687 ≈ (2 + 6/7)+18 12694 ≈ 4 × (69/2 – 1) 12703 ≈ (70 / 3)1+2 12867 ≈ (8 – 1)7 / 26 12945 ≈ (9+5/(2+1))4 (JD) 13178 ≈ 731/8 + 1 13467 ≈ 1437/6 13647 ≈ 34×(1+7/6) 13648 ≈ 38+4/6+1 (JD) 13724 ≈ 134 – 2/7 13823 ≈ (3 × 8)3 – 1 / 2 13824 ≈ 243 + 1 / 8 13985 ≈ 91+5 / 38 13986 ≈ 96 / 38 + 1 14273 ≈ 134 / 2 – 7 14376 ≈ 316/7 – 4 14641 ≈ 114 + 4/6 14649 ≈ 4/(1–(6–(9–4))) (JD) 14755 ≈ 547/5 – 1 14759 ≈ (95 – 7) / 4 – 1 14762 ≈ (7 + 2)6–1 / 4 (BH) 14768 ≈ 4 × 86 / 71 14769 ≈ 96–1 / 4 + 7 14987 ≈ 184 / / – 9 14996 ≈ (2 × 9)4 / (1 + 6) 14997 ≈ (9 + 9)4 / 7 + 1 15216 ≈ (2 × 6 / 5)11 15297 ≈ 2/(97–5–1) (JD) 15572 ≈ 75 – 2/51 15612 ≈ 56–(2–11) (JD) 15622 ≈ 56 – 2 – 1/2 15623 ≈ -1 + 56 – 2/3 15624 ≈ -1 + 56 + 2/4 15625 ≈ 1 × 56 + 2/5 15626 ≈ 1 + 56 + 2/6 15627 ≈ -1 + 56 + 7/2 15628 ≈ 56 + (8 – 1) / 2 15629 ≈ 56 + 9 × 1 / 2 15633 ≈ (5+13–3)6 (JD) 15634 ≈ 56+14–3 (JD) 15636 ≈ 56+3-1–6 (BH) 15637 ≈ 1 + 56+3-7 (BH) 15654 ≈ (5+5–4)6–1 (JD) 15655 ≈ (5+51–5)6 (JD) 15682 ≈ (18–2+5)6 (JD) 15747 ≈ 47 – 1/(5×7) 15772 ≈ (2–7+5)7–1 (JD) 15793 ≈ 39 – 1/5 – 7 15794 ≈ 1/(4–9+7–5) (JD) 15860 ≈ (5 + 1/80)6 15903 ≈ (90 / 13)5 15906 ≈ 56 + 1/90 15962 ≈ (6 × (9 – 1))5/2 16258 ≈ 56 + 2/81 16345 ≈ 4 × 531/6 16382 ≈ (86–1 – 3) / 2 16384 ≈ 48–1 + 3/6 16389 ≈ 39 – 18/6 16432 ≈ 3142 / 6 16472 ≈ 47+16–2 (JD) 16474 ≈ 6441/7 16497 ≈ (6 × 17 / 9)4 16547 ≈ (7 – 1/46)5 16742 ≈ 47 + 1/26 16754 ≈ 76–(5–4+1) (JD) 16759 ≈ 69×5/7 – 1 16783 ≈ (7–(8–3))6–1 (JD) 16797 ≈ (76 – 1) / 7 – 9 16834 ≈ 1 × (6 / 4)3×8 17247 ≈ 47 + 1/27 17275 ≈ 2/(1–(7–(7–5))) (JD) 17529 ≈ 175/(92) (JD) 17542 ≈ (4 + 2/51)7 17567 ≈ (5 + 7/71)6 17689 ≈ 961 + 8/7 17856 ≈ 8 × 56 / 7 – 1 17857 ≈ 8 × 57–1 / 7 17865 ≈ 8 × (56 / 7 + 1) 17928 ≈ (9 / 71/2)8 18183 ≈ (8/3)1+1+8 (BH) 18532 ≈ 183 + 2/5 18592 ≈ 58 / 21 – 9 18599 ≈ (9 / 81/9)5 18724 ≈ 1 × 2 × 48 / 7 18932 ≈ 2/(1–(8–(3–9))) (JD) 19175 ≈ (5 × 9 / 11)7 19242 ≈ (12 – 2/9)4 19453 ≈ (3–(41–5))9 (JD) 19467 ≈ ((7+4)6)/91 (JD) 19483 ≈ 419 × 3 / 8 19682 ≈ (1 + 2)9 – 8/6 19683 ≈ 39 + 1 – 6/8 19684 ≈ (4 – 1)9 + 8/6 19813 ≈ 1 × (31 / 9)8 19847 ≈ (1 / 9 + 8 – 4)7 (JD) 19966 ≈ 66 – 9/19 19972 ≈ 2(99+1)/7 19984 ≈ 49 / 81/9 20995 ≈ (9×2)5/90 (JD) 21437 ≈ ((7×(4+1))3)/2 (JD) 21556 ≈ 56+1/5–2 (JD) 21558 ≈ 51/5+8–2 (JD) 21647 ≈ 6(41–2)/7 (JD) 21741 ≈ (12+1/7)4 (JD) 21798 ≈ 891–2/7 (JD) 21843 ≈ 48/3–2×1 (JD) 21844 ≈ (48–2)/(4–1) (JD) 21845 ≈ 2 × 48 / (1 + 5) (BH) 21846 ≈ 48×2/6+1 (JD) 21847 ≈ (48+7)/(2+1) (JD) 21859 ≈ (2–1/5)9+8 (JD) 22143 ≈ 312/24 (JD) 22185 ≈ ((8+1/2)5)/2 (JD) 22518 ≈ (2/(2+5×1))–8 (JD) 22684 ≈ 4262/8 (JD) 23152 ≈ 213×5/2 (JD) 23326 ≈ (63×2–3)/2 (JD) 23527 ≈ 73×2/5–2 (JD) 23529 ≈ ((9–2)3×2)/5 (JD) 23565 ≈ (6×5)3–(5–2) (JD) 23596 ≈ (6×2/9)35 (JD) 23642 ≈ (62/(3+2))4 (JD) 23645 ≈ (62/5)4+3 (JD) 23675 ≈ 5273/6 (JD) 23757 ≈ 7×(37+2/5) (JD) 23767 ≈ ((62–7)3)/7 (JD) 23782 ≈ 8273/2 (JD) 23841 ≈ ((4+1)/2)8+3 (JD) 23845 ≈ (5/2)8+3+4 (JD) 23943 ≈ (4×3)9/2/3 (JD) 23959 ≈ (((9+2)/3)9)/5 (JD) 24279 ≈ ((7+4)9/2)/2 (JD) 24287 ≈ 722/8+4 (JD) 24385 ≈ (8×2)5/43 (JD) 24389 ≈ 293+4/8 (JD) 24414 ≈ (((4+1)4)/4)2 (JD) 24415 ≈ (54/4)2+1 (JD) 24519 ≈ 94+1–2/5 (JD) 24573 ≈ (47×3–5)/2 (JD) 24593 ≈ (39/4–2)×5 (JD) 24735 ≈ (7+(3/4)2)5 (JD) 24743 ≈ 3247/4 (JD) 24745 ≈ 544/7–2 (JD) 24747 ≈ (7–2)44/7 (JD) 24864 ≈ 4462/8 (JD) 24894 ≈ (((9+4)/4)8)×2 (JD) 25069 ≈ (950/6)2 (JD) 25226 ≈ 625/2–2 (JD) 25228 ≈ (8–2)25/2 (JD) 25251 ≈ (5/2–1)25 (JD) 25253 ≈ (3/2)5×5+2 (JD) 25287 ≈ 852×7/2 (JD) 25355 ≈ (2+5+3/5)5 (JD) 25357 ≈ (7+3/5)5+2 (JD) 25358 ≈ (8–2/5)5+3 (JD) 25384 ≈ 483–(5–2) (JD) 25396 ≈ 69/2×(5+3) (JD) 25488 ≈ (85/8)4×2 (JD) 25664 ≈ 6×(46+2–5) (JD) 25683 ≈ 8+65+2/3 (JD) 25697 ≈ 59/76–2 (JD) 26353 ≈ 3632/5 (JD) 26357 ≈ (75–2/6)×3 (JD) 26564 ≈ 266/4+5 (JD) 26578 ≈ 5728/6 (JD) 26689 ≈ (82/(9+6))6 (JD) 26779 ≈ 797×2/6 (JD) 26843 ≈ (26/(8–3))4 (JD) 26944 ≈ 429/4×6 (JD) 27183 ≈ (7/12+3)8 (JD) 27374 ≈ (7/23+4)7 (JD) 27456 ≈ 7/(42–5–6) (JD) 27535 ≈ ((5+5–2)7)/3 (JD) 27594 ≈ 49/(7+5/2) (JD) 27673 ≈ (7–3/2)6–7 (JD) 27862 ≈ 86/(22/7) (JD) 27873 ≈ ((8×7+2)3)/7 (JD) 27884 ≈ 288/7+4 (JD) 27958 ≈ (8–(27–9))5 (JD) 28379 ≈ 97×2/3–8 (JD) 28387 ≈ 38×7/(8–2) (JD) 28526 ≈ 28×2–6/5 (JD) 28571 ≈ (7–2)51/8 (JD) 28654 ≈ 85–4/62 (JD) 28674 ≈ (84+2/6)×7 (JD) 28935 ≈ 58×2/9/3 (JD) 29127 ≈ 217×2/9 (JD) 29504 ≈ (95–40)/2 (JD) 29512 ≈ 95/2–12 (JD) 29516 ≈ (95 – 16) / 2 (BH) 29517 ≈ (2/(95))–1–7 (JD) 29519 ≈ (95 – 1 – 9) / 2 (BH) 29521 ≈ –(2–95/2+1) (JD) 29522 ≈ (-2 + 95 – 2) / 2 (BH) 29523 ≈ 2 + 95 / 2 – 3 (BH) 29524 ≈ ((2/9)–5)×(24) (JD) 29525 ≈ (95 + 5/2) / 2 (BH) 29526 ≈ (95 + 6 – 2) / 2 (BH) 29528 ≈ 95/2+8/2 (JD) 29532 ≈ 23+95/2 (JD) 29533 ≈ 95/2+3×3 (JD) 29539 ≈ (25/9)9×3 (JD) 29548 ≈ (95 + 48) / 2 (BH) 29582 ≈ 95/(2–(2–8)) (JD) 29588 ≈ 95/2+8×8 (JD) 29663 ≈ ((9/2+3)6)/6 (JD) 29678 ≈ 2(98+6)/7 (JD) 29747 ≈ (7/2)74/9 (JD) 29817 ≈ (29/8)1+7 (JD) 29818 ≈ (29/8)8+1 (JD) 29861 ≈ (2–1/6)9+8 (JD) 29917 ≈ (29/7–1)9 (JD) 30291 ≈ 2031/9 (JD) 31398 ≈ 913/8/3 (JD) 31433 ≈ 314–3+3 (JD) 31462 ≈ (3×1/4)–(62) (JD) 31463 ≈ (4/3)36+1 (JD) 31676 ≈ (3/(7+1)–6)6 (JD) 31795 ≈ 95×7/13 (JD) 32238 ≈ 3823–2 (JD) 32267 ≈ ((7–2/3)6)/2 (JD) 32413 ≈ 214/(3+3) (JD) 32415 ≈ 215–(4–3) (JD) 32416 ≈ 214/6+3 (JD) 32547 ≈ (7+2–(4–3))5 (JD) 32747 ≈ 2/(43–7–7) (JD) 32756 ≈ (7–6+2–3)–5 (JD) 32765 ≈ (6+2)5–7/3 (JD) 32768 ≈ 6/7+83+2 (JD) 32778 ≈ 23–7+8+7 (JD) 32785 ≈ (3/2)7+85 (JD) 32859 ≈ 89–3+5–2 (JD) 33214 ≈ (33/2)4–1 (JD) 33215 ≈ (33/2)–(1–5) (JD) 33684 ≈ 643/(8+3) (JD) 33688 ≈ ((8+3–3)6)/8 (JD) 33796 ≈ (97/3)3–6 (JD) 34328 ≈ (32+4/8)3 (JD) 34576 ≈ (34/7)5/6 (JD) 34865 ≈ (4+3)6–5/8 (JD) 34952 ≈ 49×2/5/3 (JD) 34989 ≈ ((9+9)4–8)/3 (JD) 34991 ≈ ((9+9)4–1)/3 (JD) 34992 ≈ ((9+9)4+2)/3 (JD) 35187 ≈ (58/13)7 (JD) 35374 ≈ (3×(5–3/7))4 (JD) 35391 ≈ (9–1)5+3–3 (JD) 35427 ≈ (37+4)/5–2 (JD) 35429 ≈ (39+4–2)/5 (JD) 35511 ≈ (55+3)/11 (JD) 35547 ≈ ((5+4+3)5)/7 (JD) 35676 ≈ (7/6)65+3 (JD) 35844 ≈ 48–(4–(3/5)) (JD) 35874 ≈ (8+3–(7/4))5 (JD) 35893 ≈ 39+5–(3/8) (JD) 35982 ≈ (9+2)35/8 (JD) 36141 ≈ (11/4+3)6 (JD) 36142 ≈ (23/4)6+1 (JD) 36514 ≈ (5+3–(1/4))6 (JD) 36718 ≈ 873–(1/6) (JD) 36856 ≈ 66–5/38 (JD) 37275 ≈ (7+3)25/7 (JD) 37363 ≈ (33/6)7–3 (JD) 37366 ≈ (6–3×3/6)7 (JD) 37369 ≈ (9×3/6)7+3 (JD) 37446 ≈ ((4+4)6)/7–3 (JD) 37448 ≈ (48×4–3)/7 (JD) 37449 ≈ 49/7+3/4 (JD) 37525 ≈ ((5+2/3)7)/5 (JD) 37553 ≈ 735/3/5 (JD) 37579 ≈ ((77–3)/9)5 (JD) 37679 ≈ (37/6)7/9 (JD) 37959 ≈ (93×5)9/7 (JD) 38224 ≈ 4(8/3)2×2 (JD) 38414 ≈ (3–8–14)4 (JD) 38416 ≈ 1/3+(8+6)4 (JD) 38427 ≈ ((3–8+2)×7)4 (JD) 38451 ≈ 48–5/13 (JD) 38466 ≈ (6–3+8+6)4 (JD) 38548 ≈ (8×(84–3))5 (JD) 38554 ≈ (5×4)5/83 (JD) 38837 ≈ 387/3×8 (JD) 39216 ≈ ((9–2)6+1)/3 (JD) 39364 = (39 × 6 – 4) / 3 (BH) 39368 = (39 × 6 + 8) / 3 (BH) 39442 ≈ 39×(4–4+2) (JD) 39506 ≈ (60/9)5×3 (JD) 39523 ≈ 39×(5–3+2) (JD) 39687 ≈ (39/7)8/6 (JD) 39761 ≈ 713/9–6 (JD) 39767 ≈ ((77–6)3)/9 (JD) 39782 ≈ 792–(3/8) (JD) 39932 ≈ (((9+2)/3)9)/3 (JD) 40634 ≈ 404/63 (JD) 41283 ≈ 48–1/3–2 (JD) 41285 ≈ 48/(2+1)+5 (JD) 41286 ≈ 48–2/6+1 (JD) 42356 ≈ 65×(42–3) (JD) 42459 ≈ 59/(44+2) (JD) 42537 ≈ (3/7+4×2)5 (JD) 42559 ≈ (9×5)4/5+2 (JD) 42798 ≈ (87–2)/49 (JD) 43581 ≈ (4+3/5)8–1 (JD) 43682 ≈ 432/6–8 (JD) 43686 ≈ (86–3)/6–4 (JD) 43689 ≈ (49+3–8)/6 (JD) 43690 ≈ 49/6+3×0 (JD) 43691 ≈ (49+3+1)/6 (JD) 43692 ≈ 49/6+3/2 (JD) 43693 ≈ (49–3)/6+3 (JD) 43694 ≈ (49+4)/6+3 (JD) 43695 ≈ (49–3)/6+5 (JD) 43696 ≈ (36+49)/6 (JD) 43697 ≈ (49–3)/6+7 (JD) 43698 ≈ (49–3)/6+8 (JD) 43699 ≈ 9+(49–3)/6 (JD) 43983 ≈ 833/(9+4) (JD) 43987 ≈ (9×8)(7+3)/4 (JD) 44205 ≈ (50/4+2)4 (JD) 44389 ≈ ((8–3)9)/44 (JD) 44467 ≈ 7(6+4×4)/4 (JD) 44841 ≈ ((4+1)/4)48 (JD) 44845 ≈ (5/4)48+4 (JD) 44937 ≈ 443/7×9 (JD) 44971 ≈ 941/7×4 (JD) 45267 ≈ (4+5/(2+6))7 (JD) 45295 ≈ 9×((5+2/4)5) (JD) 45437 ≈ 734/(54) (JD) 45478 ≈ (4–5/4/7)8 (JD) 45569 ≈ (94/(6+5))5 (JD) 45687 ≈ 57–8/6/4 (JD) 45696 ≈ 9+56+4/6 (JD) 45858 ≈ (84/5)8/5 (JD) 45875 ≈ 48×7/(5+5) (JD) 45927 ≈ 94×7+2/5 (JD) 46272 ≈ ((7+2/6)×2)4 (JD) 46332 ≈ (63–3/4)2 (JD) 46356 ≈ (6/(34–5))6 (JD) 46357 ≈ 46(3+5)/7 (JD) 46372 ≈ 2(6/4)7/3 (JD) 46467 ≈ (4–4–6)6–7 (JD) 46486 ≈ 66/(48–4) (JD) 46529 ≈ (4–(2–9)+5)6 (JD) 46566 ≈ 66/(46–5) (JD) 46567 ≈ 66–(4–5)–7 (JD) 46573 ≈ (35–4–7)6 (JD) 46579 ≈ 69–(7–4)+5 (JD) 46617 ≈ 6(1–4)–7+6 (JD) 46618 ≈ (1/6–4)8–6 (JD) 46635 ≈ 66–((5+3)–4) (JD) 46637 ≈ 66–73/4 (JD) 46638 ≈ 66–(8–4)+3 (JD) 46639 ≈ 66–49/3 (JD) 46643 ≈ 66–(3–(4+4)) (JD) 46644 ≈ ((4+4)–4–6)6 (JD) 46647 ≈ 66–((7–4)/4) (JD) 46648 ≈ 4–4+66–8 (JD) 46649 ≈ 66–9/4–4 (JD) 46651 ≈ –(4–66+5–1) (JD) 46652 ≈ –(4–(66+5–2)) (JD) 46653 ≈ –(4–66–5/3) (JD) 46654 ≈ (4×(66)–5)/4 (JD) 46655 ≈ –((4–66×5)/5) (JD) 46656 ≈ 4/6+65×6 (JD) 46657 ≈ 65×6+7/4 (JD) 46658 ≈ 66+5×4/8 (JD) 46659 ≈ 4+66–5/9 (JD) 46661 ≈ 66+6–1/4 (JD) 46662 ≈ 26/4+66 (JD) 46663 ≈ 43/6+66 (JD) 46664 ≈ 66+(6+4)–4 (JD) 46665 ≈ 46/5+66 (JD) 46666 ≈ 64/6+66 (JD) 46667 ≈ 64–7+6+6 (JD) 46668 ≈ 66+4–6–8 (JD) 46669 ≈ 66+9×6/4 (JD) 46673 ≈ (3–7+6)6–4 (JD) 46674 ≈ 74/4+66 (JD) 46675 ≈ 64/(75)+6 (JD) 46676 ≈ (67+4–6)/6 (JD) 46677 ≈ ((7–4)–7+6)6 (JD) 46678 ≈ (8/(47)+6)6 (JD) 46681 ≈ (4–8–1/6)–6 (JD) 46683 ≈ ((8+4)–3+6)6 (JD) 46692 ≈ ((9×4)–2+6)6 (JD) 46762 ≈ 6(7×4)–2+6 (JD) 46846 ≈ 8+(6+4–4)6 (JD) 46997 ≈ 9×(67/9+4) (JD) 47235 ≈ (73/4×2)5 (JD) 47388 ≈ (8×3)4/7–8 (JD) 47396 ≈ (4×3)6/9/7 (JD) 47823 ≈ ((4–(8–2))7)×3 (JD) 48399 ≈ 98/(34/9) (JD) 48616 ≈ 48/(61/6) (JD) 48738 ≈ 38×(8–4/7) (JD) 48795 ≈ 89/47+5 (JD) 48819 ≈ ((4+1)8)/8–9 (JD) 48825 ≈ (58–24)/8 (JD) 48827 ≈ ((7–2)8–4)/8 (JD) 48831 ≈ ((4+1)8)/8+3 (JD) 48832 ≈ ((3+2)8)/8+4 (JD) 48835 ≈ 58/8+4+3 (JD) 48852 ≈ 24+58/8 (JD) 48875 ≈ 47+58/8 (JD) 48913 ≈ 89/(143) (JD) 48972 ≈ 79/824 (JD) 49265 ≈ 295/4–6 (JD) 49285 ≈ 24(9+8)/5 (JD) 49436 ≈ 96×4/43 (JD) 49658 ≈ 86/5+4–9 (JD) 51289 ≈ (9–2/8)5–1 (JD) 51397 ≈ (5–9/31)7 (JD) 51398 ≈ 59×1/38 (JD) 51794 ≈ (9+1)5/7+4 (JD) 52245 ≈ 5(5+22)/4 (JD) 52247 ≈ 527/4+2 (JD) 52376 ≈ 6325/7 (JD) 52426 ≈ (4×2)6/5–2 (JD) 52428 ≈ 28×2×4/5 (JD) 52429 ≈ 49/5+2/2 (JD) 52449 ≈ 94–(5–2)+4 (JD) 52674 ≈ ((7–2/6)5)×4 (JD) 52732 ≈ (75/2)3–2 (JD) 52734 ≈ 753/4/2 (JD) 52756 ≈ (52/(6+5))7 (JD) 53269 ≈ 95–3/(26) (JD) 53429 ≈ (9+5)4+2–3 (JD) 53476 ≈ 76/(3–4/5) (JD) 53657 ≈ 7/(65–3–5) (JD) 53683 ≈ ((8+6–3)5)/3 (JD) 53872 ≈ ((83+7)2)/5 (JD) 54557 ≈ –((5/4/5–5)7) (JD) 54618 ≈ (48/6+1)×5 (JD) 54687 ≈ 56×7×4/8 (JD) 54779 ≈ 9×(47–5/7) (JD) 54889 ≈ (54/9/8)–8 (JD) 55129 ≈ 95–(2–5)–1 (JD) 55492 ≈ (42×5/9)5 (JD) 55789 ≈ 58/7–9–5 (JD) 55794 ≈ (5×5)4/7–9 (JD) 55797 ≈ (5×(57–9))/7 (JD) 55987 ≈ ((9+5–8)7)/5 (JD) 56328 ≈ ((8–2/6)×5)3 (JD) 56339 ≈ ((9+3)6)/53 (JD) 56485 ≈ (55/6)4×8 (JD) 56623 ≈ (6×(6+2/5))3 (JD) 56667 ≈ (7–(5/6)+6)6 (JD) 56842 ≈ 5842/6 (JD) 57397 ≈ (9/(77–3))5 (JD) 57683 ≈ (63/8+7)5 (JD) 57782 ≈ (8+7–(7–2))5 (JD) 58368 ≈ 68–5×3/8 (JD) 58416 ≈ 846×1/5 (JD) 58793 ≈ (9–(8–(7/3)))5 (JD) 58920 ≈ (9–(20–8))5 (JD) 58921 ≈ (9–(2–8))5+1 (JD) 58922 ≈ 95–(2–(8+2)) (JD) 58923 ≈ (9–(2–8))5+3 (JD) 58924 ≈ (9–(2–8))5+4 (JD) 58925 ≈ (9–(2–8))5+5 (JD) 58926 ≈ (9–(2–8))5+6 (JD) 58927 ≈ (9–(2–8))5+7 (JD) 58928 ≈ (9–(2–8))5+8 (JD) 58929 ≈ 9+(9–(2–8))5 (JD) 58963 ≈ 95–83/6 (JD) 58975 ≈ 85×9/5–7 (JD) 58984 ≈ (9–8/(84))5 (JD) 58992 ≈ (9–(2–9))5+8 (JD) 58993 ≈ 9+(9–(8–3))5 (JD) 59028 ≈ 95–(80–2) (JD) 59032 ≈ 95–(20–3) (JD) 59047 ≈ 95+0–7/4 (JD) 59048 ≈ 95–8/40 (JD) 59049 ≈ 9/40+95 (JD) 59065 ≈ 960–5+5 (JD) 59112 ≈ 95+2–11 (JD) 59227 ≈ 927–2+5 (JD) 59254 ≈ 95+5–4–2 (JD) 59256 ≈ 952–6+5 (JD) 59289 ≈ 95×(82–9) (JD) 59296 ≈ 92–9+5–6 (JD) 59434 ≈ (9+3/(44))5 (JD) 59563 ≈ (9+(5–3)–6)5 (JD) 59585 ≈ 9(8–5)–5+5 (JD) 59586 ≈ 58/(5/9+6) (JD) 59604 ≈ 506/(49) (JD) 59652 ≈ 962–5+5 (JD) 59677 ≈ 77×5/69 (JD) 59721 ≈ (9+7–2)5×1 (JD) 59757 ≈ ((7+7)5–5)/9 (JD) 61444 ≈ 444/61 (JD) 61449 ≈ 69/4/41 (JD) 61677 ≈ (7+(1–6)/7)6 (JD) 62016 ≈ 6102/6 (JD) 62495 ≈ 56×4–9/2 (JD) 62849 ≈ 968–2+4 (JD) 63248 ≈ 48/(26–3) (JD) 63259 ≈ (9+2–3)5–6 (JD) 63728 ≈ (38×2)7/6 (JD) 63774 ≈ (6/7+4)7–3 (JD) 63777 ≈ (6/7+7–3)7 (JD) 63887 ≈ (8–3)7/8+6 (JD) 64423 ≈ 46+2–(3–4) (JD) 64532 ≈ (5+4/3)6–2 (JD) 64534 ≈ (4+4–5/3)6 (JD) 64538 ≈ (8–5/3)6+4 (JD) 64813 ≈ 48+(1–6)–3 (JD) 64931 ≈ (6–3–4)9–1 (JD) 65089 ≈ (58–90)/6 (JD) 65259 ≈ (9+2/(6+5))5 (JD) 65329 ≈ 562/9–3 (JD) 65332 ≈ 562/3/3 (JD) 65338 ≈ (33–6–5)8 (JD) 65434 ≈ (6–4–4)5+3 (JD) 65521 ≈ 216–(5–5) (JD) 65534 ≈ 45+3–6/5 (JD) 65541 ≈ (5–5+16)4 (JD) 65867 ≈ 67/(5–6/8) (JD) 65912 ≈ 2/(1–(6–(9–5))) (JD) 66429 ≈ (96–4)/(6+2) (JD) 67473 ≈ 7(6+34)/7 (JD) 67723 ≈ ((7–3)×6)7/2 (JD) 67865 ≈ ((8+5/6)6)/7 (JD) 68294 ≈ (284–6)/9 (JD) 68347 ≈ (86/7)4×3 (JD) 68354 ≈ (68/5+4)×3 (JD) 68955 ≈ 96/85+5 (JD) 69318 ≈ 96/(8–1/3) (JD) 69475 ≈ 6(7+4)/9+5 (JD) 69578 ≈ 97–(8/6)+5 (JD) 69754 ≈ (59+6)/(7×4) (JD) 69877 ≈ (6–(8/7)7)9 (JD) 69985 ≈ 65×9+9/8 (JD) 70795 ≈ 79/570 (JD) 71583 ≈ (8+713)/5 (JD) 71632 ≈ ((7/3)2+1)6 (JD) 71968 ≈ (9+1)6–8/7 (JD) 72326 ≈ 76–(2–2)–3 (JD) 72329 ≈ 79–(3+2–2) (JD) 72469 ≈ 97/(64+2) (JD) 73528 ≈ (82/7)5/3 (JD) 73542 ≈ (3–(5–2)+4)7 (JD) 73559 ≈ 37+5–9/5 (JD) 73584 ≈ (48+3)/57 (JD) 74229 ≈ 94×(27/2) (JD) 74384 ≈ (3/47+4)8 (JD) 74513 ≈ 57–1/34 (JD) 74689 ≈ 86/(94/7) (JD) 74733 ≈ (37+7)/(43) (JD) 74858 ≈ 8×(48/7–5) (JD) 74882 ≈ 8×(48/7–2) (JD) 74889 ≈ 48×8/7–9 (JD) 74897 ≈ (87–9)/(7×4) (JD) 74898 ≈ 87/(9×4–8) (JD) 74952 ≈ (5–4+2/7)–9 (JD) 74963 ≈ (4×3)(9/7)6 (JD) 75136 ≈ (5–1/36)7 (JD) 75281 ≈ 827×1/5 (JD) 75287 ≈ 57–2/87 (JD) 75359 ≈ (5–(9–(5/3)))7 (JD) 75367 ≈ 67/(5/7+3) (JD) 75418 ≈ (4/8–7)5+1 (JD) 75645 ≈ 57/(65–4) (JD) 75915 ≈ (95+1)/7–5 (JD) 75916 ≈ 96/7+1–5 (JD) 75919 ≈ 95×9/7–1 (JD) 75920 ≈ (95+20)/7 (JD) 76229 ≈ 79/2×6×2 (JD) 76285 ≈ 76/(25/8) (JD) 76346 ≈ 76–4/6/3 (JD) 76431 ≈ (6–(4–3+1))7 (JD) 76449 ≈ 4(6+4)/9+7 (JD) 76735 ≈ 576–(3–7) (JD) 77345 ≈ 573–(7–4) (JD) 77415 ≈ 571–(7–4) (JD) 77645 ≈ 764–7/5 (JD) 78124 ≈ (4+1)7–2/8 (JD) 78125 ≈ 8/21+57 (JD) 78145 ≈ 81/4+57 (JD) 78154 ≈ 58–4+7–1 (JD) 78155 ≈ 581–5+7 (JD) 78329 ≈ 893/(7+2) (JD) 78335 ≈ (8–3+5)7–3 (JD) 78338 ≈ (8–3+8–3)7 (JD) 78349 ≈ (9×8)4/(73) (JD) 78365 ≈ 5(63–8)×7 (JD) 78422 ≈ (22–8+4)7 (JD) 78553 ≈ ((5–3)–8+5)7 (JD) 78562 ≈ 5(6–2)/8+7 (JD) 78945 ≈ 57+94/8 (JD) 79485 ≈ (9–(8/4)+5)7 (JD) 79592 ≈ 79/(29–5) (JD) 79889 ≈ 88–((9+9)/7) (JD) 82653 ≈ (8/5+3+2)6 (JD) 82655 ≈ (8/5+5)6+2 (JD) 83547 ≈ 78/(5+43) (JD) 83799 ≈ 398/7/9 (JD) 83984 ≈ (9+8)8–3+4 (JD) 84776 ≈ 78/(74–6) (JD) 84979 ≈ (7/8)9–94 (JD) 85222 ≈ ((5–2)/2)28 (JD) 86362 ≈ ((2–6–8)6)/3 (JD) 86475 ≈ 48+(7–6)/5 (JD) 86507 ≈ (68/7)5+0 (JD) 86594 ≈ 8×((6/5+9)4) (JD) 86776 ≈ ((7+6)/7–6)8 (JD) 87356 ≈ (86–75)/3 (JD) 87367 ≈ 86/3–7–7 (JD) 87376 ≈ (86+7)/3–7 (JD) 87381 ≈ 87/3/8×1 (JD) 87383 ≈ ((8×8)3+7)/3 (JD) 87386 ≈ (86+8+7)/3 (JD) 87459 ≈ 49–(5/7)+8 (JD) 87504 ≈ (7/5)40/8 (JD) 87732 ≈ ((87–2)3)/7 (JD) 89651 ≈ (51/9/8)–6 (JD) 89680 ≈ 98/8/60 (JD) 90846 ≈ (90/6+4)8 (JD) 91747 ≈ 49–(7–(1/7)) (JD) 92425 ≈ ((5/4)2+2)9 (JD) 92681 ≈ 218–9/6 (JD) 92687 ≈ 89–7/2+6 (JD) 92689 ≈ 299/6+8 (JD) 93753 ≈ (3/7+9×5)3 (JD) 94527 ≈ (25/7)9–4 (JD) 94576 ≈ (7/4+5)6–9 (JD) 94726 ≈ 79/426 (JD) 94786 ≈ 6987/4 (JD) 94985 ≈ (5/9+9+8)4 (JD) 95385 ≈ 5(9/5)3×8 (JD) 95536 ≈ 365–9/5 (JD) 95648 ≈ 49–(8/(6+5)) (JD) 95659 ≈ 96/(5/9+5) (JD) 96625 ≈ 96×2/(6+5) (JD) 96824 ≈ (89/6)4×2 (JD) 96835 ≈ 9+(6/5+3)8 (JD) 97353 ≈ ((93–5)3)/7 (JD) 97365 ≈ (6/5)9×7–3 (JD) 97367 ≈ (77–96)/3 (JD) 97368 ≈ (6/(8–3))9×7 (JD) 97526 ≈ 2/(9–5+6–7) (JD) 98753 ≈ ((7/9+5)×8)3 (JD)

Non-Integral Friedman Numbers (rounding up)
 377 ≈ (3 / 7)-7 (BH) 1263 ≈ 36 + 1/2 1556 ≈ 1 × 65 / 5 2457 ≈ (7 + 5-2)4 (JD) 2476 ≈ 72-6+4 (JD) 2654 ≈ 64 + 2/5 3281 ≈ 1 × 38 / 2 3282 ≈ (2 + 1 × 38) / 2 3846 ≈ (63 / 8)4 4666 ≈ 66 / (4 + 6) 4921 ≈ (1 + 2)9 / 4 4923 ≈ 39 / 4 + 2 5344 ≈ 54×4 / 3 5462 ≈ (2 × 4)5 / 6 5642 ≈ (52 / 6)4 6755 ≈ (6 / 7 / 5)-5 (JD) 6945 ≈ 4 × 56 / 9 8296 ≈ -8 + (2 / 9)-6 (BH) 8374 ≈ 487/3 8545 ≈ 545/8 9463 ≈ 39–4/6 (BH) 11163 ≈ ((1+6) / 3)11 11223 ≈ (1 + 1/2)23 11365 ≈ 315/6 + 1 11486 ≈ ((11+8) / 4)6 11664 ≈ (-11 + 66) / 4 11665 ≈ (66 + 1) / (5 – 1) 11765 ≈ 76 / 5 / (1 + 1) 11768 ≈ (17 / 6)1+8 11769 ≈ 1 + (17 / 6)9 12448 ≈ ((1 + 2) /4 – 4)8 (JD) 12484 ≈ 4 × 48 / 21 12589 ≈ 8 × 195/2 12725 ≈ (1 + 5)7 / 22 12726 ≈ 67 / 22 + 1 12783 ≈ 713 / 28 12937 ≈ 1972 / 3 12945 ≈ (1 × 45 / 9)2 12946 ≈ ((46–1)/9)2 (JD) 12964 ≈ 96 / 41 + 2 13549 ≈ (3 – 5/41)9 13648 ≈ 1 × 38 + 4/6 13752 ≈ 135 / 27 13778 ≈ (7 – 3)7 – 1/8 13824 ≈ 243–1/8 (JD) 13986 ≈ 1× 96 / 38 14315 ≈ 453 / 11 14565 ≈ (4 × 5)16/5 14614 ≈ 114–(6–4) (JD) 14641 ≈ 114 – 4/6 14742 ≈ 2417/4 14771 ≈ (4 – 1/17)7 14786 ≈ 47 – 6/81 14997 ≈ 94 × (1 + 9/7) 15253 ≈ (-1/5 + 25)3 15259 ≈ (-1 + 5) / (2 / 5)9 15528 ≈ 55+1–(2–8) (JD) 15623 ≈ -1 + 56 – 3/2 15624 ≈ -1 + 56 – 2/4 15625 ≈ 1 × 56 – 2/5 15626 ≈ 1 × 56 + 2/6 15627 ≈ 1 + 56 + 2/7 15628 ≈ 56 + 2 + 1/8 15629 ≈ 56 + 9/2 – 1 15632 ≈ 56 + 13/2 15637 ≈ 1 × 56+3-7 (BH) 15639 ≈ 563–9+1 (JD) 15644 ≈ (4–5+4+1)6 (JD) 15645 ≈ 56–4+5+1 (JD) 15646 ≈ 1+56–4+6 (JD) 15648 ≈ ((8–4+1)×5)6 (JD) 15649 ≈ 5(9–4+1)×6 (JD) 15656 ≈ (5–6–1/5)–6 (JD) 15743 ≈ 47×(1–(3–5)) (JD) 15867 ≈ (5 + 1/78)6 16288 ≈ (1/6 – 2)8+8 (JD) 16327 ≈ 631/2 / 7 16374 ≈ 46+1–(3–7) (JD) 16384 ≈ 48–1 – 3/6 16385 ≈ 3 × (85 + 1) / 6 16390 ≈ 39 – 1/6 + 0 16391 ≈ 39 – 1/6 + 1 16392 ≈ 39 – 1/6 + 2 16393 ≈ 39 – 1/6 + 3 16394 ≈ 39 – 1/6 + 4 16395 ≈ 39 – 1/6 + 5 16396 ≈ 39 – 1/6 + 6 16397 ≈ 39 – 1/6 + 7 16398 ≈ 39 – 1/6 + 8 16399 ≈ 39 – 1/6 + 9 16429 ≈ 42–9+6+1 (JD) 16498 ≈ (1 + 9 + 8/6)4 16582 ≈ 516/2 / 8 16583 ≈ (513 + 6) / 8 16742 ≈ 47+2–6–1 (JD) 16743 ≈ 47+(3–1)–6 (JD) 16745 ≈ (6 / 51/4)7 16752 ≈ (7–(6–(2+1)))5 (JD) 16753 ≈ (7–(6–3))5+1 (JD) 16763 ≈ 76–(3–6+1) (JD) 16773 ≈ (7–(7–3))6–1 (JD) 16834 ≈ (6 / 4)3×8 – 1 16835 ≈ (6 / (5 – 1))3×8 16950 ≈ 106/59 (JD) 17134 ≈ 47 + 1/31 17257 ≈ (7 + 1/27)5 17491 ≈ 1 × (7 + 9 / 2)4 17492 ≈ (7 + 9 / 2)4 + 1 17528 ≈ (7 / 2)8 – 1/5 17854 ≈ (17 / 5)8 – 4 17858 ≈ 178 / 58 (JD) 17866 ≈ 86 – 61/7 17895 ≈ (18 – 7)5 / 9 18276 ≈ (7 / 2)8 – 1/6 18574 ≈ (41 / 8)7 / 5 18724 ≈ 2 × 48 / 7 – 1 18725 ≈ 2 × (5 – 1)8 / 7 18726 ≈ 86 / (2 × 7) + 1 18939 ≈ 913/(89) (JD) 19227 ≈ (2+1–(2–7))9 (JD) 19247 ≈ (4–1)9–(7–2) (JD) 19307 ≈ (1 + 9)30/7 (JD) 19368 ≈ 39 – 1/68 19373 ≈ (3 × 9 – 1/7)3 19382 ≈ ((2 + 9) / 8)31 19482 ≈ 819/4 – 2 19484 ≈ 41 + 49/8 19532 ≈ 59–2 / (3 + 1) (BH) 19643 ≈ (93 – 1)6/4 19682 ≈ (6 / 2)9 – 1/8 19683 ≈ 39 + 1 – 8/6 19684 ≈ (4 – 1)9 + 6/8 19693 ≈ 39 + 9 + 1/6 19813 ≈ (31 / 9)8 – 1 21375 ≈ (731/5)2 (JD) 21386 ≈ (6–2+3)8+1 (JD) 21705 ≈ (5/7+2)10 (JD) 21834 ≈ 48/3–12 (JD) 21843 ≈ 48/3–2–1 (JD) 21844 ≈ 48/(4–1)–2 (JD) 21845 ≈ 48/(5–2)–1 (JD) 21846 ≈ (1 × 2 × 48) / 6 (BH) 21849 ≈ (9+48)/(2+1) (JD) 22518 ≈ ((5+2)/2)8–1 (JD) 22519 ≈ (2/(2+5))1–9 (JD) 22796 ≈ ((6+2)7)/92 (JD) 22798 ≈ 87/92+2 (JD) 22877 ≈ 77/((8–2)2) (JD) 23257 ≈ ((73–2)2)/5 (JD) 23365 ≈ 5(3/6–3)2 (JD) 23569 ≈ ((9–2+6)5)×3 (JD) 23614 ≈ (461/3)2 (JD) 23639 ≈ 39+(3–2)/6 (JD) 23657 ≈ (62–7+5)×3 (JD) 23665 ≈ (66+5–3)/2 (JD) 23842 ≈ (2/4+2)8+3 (JD) 23855 ≈ (5–(2/5)+3)8 (JD) 24347 ≈ (2×4)34/7 (JD) 24369 ≈ 293–(4–6) (JD) 24389 ≈ 293–4/8 (JD) 24415 ≈ (5/2×(4+1))4 (JD) 24587 ≈ (784/5)2 (JD) 24598 ≈ 85–4/29 (JD) 24603 ≈ 20(6/4)3 (JD) 24977 ≈ ((92+7)/7)4 (JD) 25165 ≈ ((6–1/2)5)×5 (JD) 25252 ≈ –(((2–5)/2)52) (JD) 25268 ≈ 85–(2–(6/2)) (JD) 25313 ≈ ((5×3)3+1)/2 (JD) 25314 ≈ (5×3)4/2+1 (JD) 25327 ≈ (375–2)/2 (JD) 25356 ≈ ((6+32)/5)5 (JD) 25358 ≈ (38/5)5+2 (JD) 25368 ≈ (38–2/5)×6 (JD) 25576 ≈ 76/(5–2/5) (JD) 25620 ≈ (60–2)5/2 (JD) 25638 ≈ 8326/5 (JD) 25668 ≈ ((8/6)6+2)5 (JD) 25676 ≈ 66/(7+2)+5 (JD) 25719 ≈ (91/5)7/2 (JD) 25743 ≈ (2/3+7+5)4 (JD) 26215 ≈ 216×2/5 (JD) 26427 ≈ (2–2–7–6)4 (JD) 26573 ≈ (37/6)2/5 (JD) 26677 ≈ 676/7×2 (JD) 26732 ≈ (22/6)7×3 (JD) 26751 ≈ (5–2+1/7)–6 (JD) 26853 ≈ 85/(63–2) (JD) 27319 ≈ (29/17)3 (JD) 27338 ≈ 7(3–3/8)×2 (JD) 27341 ≈ 721/4+3 (JD) 27438 ≈ 873/24 (JD) 27575 ≈ 75×(25/7) (JD) 27674 ≈ ((7+4)/2)6–7 (JD) 27681 ≈ (12/8–7)6 (JD) 27689 ≈ (9–7/2)6+8 (JD) 27963 ≈ 69–23/7 (JD) 28337 ≈ ((83–7)/3)2 (JD) 28349 ≈ (4/3)28×9 (JD) 28358 ≈ (5/3)8×2×8 (JD) 28386 ≈ 38+8/6–2 (JD) 28388 ≈ 38+8/(8–2) (JD) 28396 ≈ 39+2/6+8 (JD) 28459 ≈ (8–2/9)5–4 (JD) 28527 ≈ (8/2)7+2/5 (JD) 28529 ≈ (95–(8–2))/2 (JD) 28572 ≈ (((2+8)5)/7)×2 (JD) 28587 ≈ 7588–2 (JD) 28657 ≈ 56×(27/8) (JD) 28674 ≈ (46+2/8)×7 (JD) 29128 ≈ 812/2/9 (JD) 29129 ≈ 29×2/9+1 (JD) 29149 ≈ 21+49/9 (JD) 29284 ≈ (9+224)/8 (JD) 29349 ≈ 39+4/(9+2) (JD) 29438 ≈ 9×((3/4+2)8) (JD) 29465 ≈ ((2+9/4)6)×5 (JD) 29467 ≈ 67/(9+2/4) (JD) 29489 ≈ 9/2×(94–8) (JD) 29517 ≈ 95/2–7–1 (JD) 29518 ≈ 95/2+1–8 (JD) 29522 ≈ –((2–95)/2+2) (JD) 29523 ≈ (2+95)/2–3 (JD) 29524 ≈ (2–95)/(2–4) (JD) 29525 ≈ 95 / 2 + 2 / 5 (BH) 29526 ≈ (95+6)/2–2 (JD) 29527 ≈ (95+7/2)/2 (JD) 29528 ≈ (95 + 8 – 2) / 2 (BH) 29545 ≈ 95/2+5×4 (JD) 29550 ≈ (95 + 50) / 2 (BH) 29567 ≈ 95/2+7×6 (JD) 29568 ≈ (86+95)/2 (JD) 29573 ≈ ((9+7–3)5)/2 (JD) 29818 ≈ (29/8)1×8 (JD) 29927 ≈ 9+(22/7)9 (JD) 30246 ≈ 6042/3 (JD) 30844 ≈ 404/83 (JD) 30964 ≈ 460/9×3 (JD) 31256 ≈ (6+51/2)3 (JD) 31462 ≈ (4/3)62–1 (JD) 31463 ≈ (4/3)36×1 (JD) 31768 ≈ (86–1)7/3 (JD) 31985 ≈ 39×(5/8+1) (JD) 32328 ≈ 323–(2–8) (JD) 32487 ≈ 234/7×8 (JD) 32566 ≈ 66–(2–3)+5 (JD) 32587 ≈ 28+7–(5–3) (JD) 32597 ≈ 39+7–(2/5) (JD) 32598 ≈ 85–29/3 (JD) 32735 ≈ ((7–(3–3))5)×2 (JD) 32746 ≈ 47×(2–(3–6)) (JD) 32748 ≈ (48–(3–7))/2 (JD) 32754 ≈ (2–(4–7))5×3 (JD) 32758 ≈ 85–7×3/2 (JD) 32768 ≈ 83+2–6/7 (JD) 32769 ≈ 3/7+29+6 (JD) 32775 ≈ (7+23–7)5 (JD) 32778 ≈ (8+3–7)7–2 (JD) 32785 ≈ 85+72/3 (JD) 32853 ≈ (8+3–5)3+2 (JD) 32855 ≈ (8+3–5)5+2 (JD) 32857 ≈ 38×(2–7+5) (JD) 32863 ≈ (8+6–3)3+2 (JD) 32865 ≈ (8+6–3)5+2 (JD) 32872 ≈ (78/3+2)2 (JD) 32943 ≈ ((93–3)/4)2 (JD) 32952 ≈ (2–(5/2)+3)9 (JD) 33216 ≈ (36/(3+1))2 (JD) 33593 ≈ (9–(3–(3–3)))5 (JD) 33645 ≈ 65×(34/3) (JD) 33769 ≈ 373×6/9 (JD) 33851 ≈ 85+(3+1)–3 (JD) 33854 ≈ 85+4–3+3 (JD) 33921 ≈ 3192/3 (JD) 34092 ≈ 32/4+9+0 (JD) 34258 ≈ (8+3/42)5 (JD) 34276 ≈ (6×4)23/7 (JD) 34461 ≈ 413/(6–4) (JD) 34529 ≈ (4+2)(9/5)3 (JD) 34659 ≈ (53/9+4)6 (JD) 34678 ≈ (48/6+7)/3 (JD) 34726 ≈ (76–(4–2))/3 (JD) 34865 ≈ 654/(83) (JD) 34886 ≈ (8×8/6+3)4 (JD) 34915 ≈ (4–(3–(1/5)))9 (JD) 34982 ≈ (9+234)/8 (JD) 34992 ≈ ((9+9)4–2)/3 (JD) 34994 ≈ ((9+9)4+4)/3 (JD) 35288 ≈ (82/5)3×8 (JD) 35386 ≈ 85+3–3–6 (JD) 35429 ≈ (39+2–4)/5 (JD) 35547 ≈ ((4×3)5–5)/7 (JD) 35595 ≈ (55/95)3 (JD) 35618 ≈ (31/8×5)6 (JD) 35653 ≈ (6×3)5/53 (JD) 35662 ≈ (36/5+2)6 (JD) 35677 ≈ (7/6)73–5 (JD) 35745 ≈ (55/4)7–3 (JD) 35869 ≈ 83/69+5 (JD) 35979 ≈ 935/9×7 (JD) 36142 ≈ (23/4)6×1 (JD) 36238 ≈ 386/(32) (JD) 36762 ≈ 66/(37–2) (JD) 36875 ≈ 38+(6+5)/7 (JD) 37364 ≈ (6×3/4)7–3 (JD) 37365 ≈ (73/6)3/5 (JD) 37367 ≈ 37×3/(67) (JD) 37398 ≈ (8/3)7×39 (JD) 37419 ≈ 49/7–31 (JD) 37446 ≈ 643/7–4 (JD) 37448 ≈ 4/7×(48–3) (JD) 37449 ≈ 49/7+3–4 (JD) 37596 ≈ (7×5–9/6)3 (JD) 37629 ≈ (9/2)7+6–3 (JD) 37641 ≈ 47+3/(6–1) (JD) 37938 ≈ ((9/7+3)8)/3 (JD) 37961 ≈ 96/(17–3) (JD) 37962 ≈ (96/7+3)/2 (JD) 38154 ≈ 85+3/41 (JD) 38414 ≈ 144–8/3 (JD) 38416 ≈ (8+6)4–1/3 (JD) 39186 ≈ 938/6+1 (JD) 39216 ≈ ((9–2)6)/3–1 (JD) 39217 ≈ (79–2–1)/3 (JD) 39328 ≈ 39×(2–(8–3)) (JD) 39365 ≈ (39 × 6 – 5) / 3 (BH) 39452 ≈ 934/5×2 (JD) 39578 ≈ 9+87/53 (JD) 39933 ≈ (33/9)9/3 (JD) 40719 ≈ (41/9)7+0 (JD) 41286 ≈ 214+8/6 (JD) 41353 ≈ 413/5×3 (JD) 42128 ≈ (821/4)2 (JD) 42543 ≈ (42/4)5/3 (JD) 42783 ≈ 78–42/3 (JD) 42798 ≈ 87/49–2 (JD) 42871 ≈ 741/8×2 (JD) 42945 ≈ (9×2)5/44 (JD) 43475 ≈ (7×5)4–4+3 (JD) 43532 ≈ (5×(3–2–3))4 (JD) 43576 ≈ (4+3/5)7–6 (JD) 43578 ≈ (8/5+3)7–4 (JD) 43661 ≈ 66–(31–4) (JD) 43679 ≈ (49–73)/6 (JD) 43683 ≈ 43×3/6–8 (JD) 43685 ≈ 85×4/3–6 (JD) 43689 ≈ (49–8–3)/6 (JD) 43690 ≈ 49/6–30 (JD) 43691 ≈ 49/6–1/3 (JD) 43692 ≈ 49/6+3–2 (JD) 43693 ≈ (9+43×3)/6 (JD) 43695 ≈ (49+5)/6+3 (JD) 43697 ≈ (37+49)/6 (JD) 43796 ≈ (9+4)7/6+3 (JD) 43963 ≈ 49/(6–(3–3)) (JD) 43988 ≈ (9×8)3–4/8 (JD) 44206 ≈ ((60–2)/4)4 (JD) 44287 ≈ 274/(8+4) (JD) 44365 ≈ (34/4)5–6 (JD) 44716 ≈ (67–1/4)/4 (JD) 44758 ≈ (87/4)4/5 (JD) 44772 ≈ (72/7)4×4 (JD) 44972 ≈ 944×2/7 (JD) 44975 ≈ (((7+4)/4)9)×5 (JD) 45296 ≈ 9×((6–2/4)5) (JD) 45438 ≈ ((8–34)/5)4 (JD) 45636 ≈ 6/(63–4–5) (JD) 45680 ≈ 540/6–8 (JD) 45688 ≈ 58×8/6–4 (JD) 45729 ≈ ((4/9+7)5)×2 (JD) 45875 ≈ (85×7–4)/5 (JD) 45876 ≈ 46×8×7/5 (JD) 45927 ≈ 94×7–2/5 (JD) 45947 ≈ ((4–5+9)4)×7 (JD) 46273 ≈ ((7×6+2)/3)4 (JD) 46341 ≈ 46+3/4+1 (JD) 46347 ≈ 47+3/4+6 (JD) 46397 ≈ (96–3+4)×7 (JD) 46523 ≈ 63×2–(5–4) (JD) 46563 ≈ ((5–3)/4–6)6 (JD) 46567 ≈ 66–54/7 (JD) 46582 ≈ (5–4+2–8)6 (JD) 46625 ≈ 66/(24–5) (JD) 46641 ≈ ((6×4–1)4)/6 (JD) 46645 ≈ 66–45/4 (JD) 46647 ≈ –(4–(66–(4–7))) (JD) 46648 ≈ 66–(8+4–4) (JD) 46651 ≈ 66–5–1/4 (JD) 46652 ≈ –(4–66+5–2) (JD) 46653 ≈ –(4–(66+5–3)) (JD) 46654 ≈ –(4–66–5/4) (JD) 46655 ≈ 65×6–5/4 (JD) 46656 ≈ –(4/6–65×6) (JD) 46657 ≈ 7/54+66 (JD) 46658 ≈ 66+(5+4)/8 (JD) 46659 ≈ 66+5×4/9 (JD) 46661 ≈ 4+66+6–1 (JD) 46662 ≈ 66+6–2/4 (JD) 46663 ≈ 66+6+3/4 (JD) 46664 ≈ (4–6+6)6–4 (JD) 46665 ≈ 66×(46–5) (JD) 46667 ≈ 66+7×6/4 (JD) 46668 ≈ ((8–4)–6+6)6 (JD) 46669 ≈ 66×(69–4) (JD) 46672 ≈ 674–2+6 (JD) 46673 ≈ (7–4+6)6–3 (JD) 46675 ≈ 75/4+66 (JD) 46678 ≈ 87/4+66 (JD) 46679 ≈ 67–(6–(9–4)) (JD) 46693 ≈ (6–4+9–3)6 (JD) 46726 ≈ 62/(74)+6 (JD) 46746 ≈ 67–(4–(6–4)) (JD) 46758 ≈ (5–(4–(6/8)))7 (JD) 46783 ≈ (4–(8–3)–7)6 (JD) 46852 ≈ ((28–6)4)/5 (JD) 46957 ≈ (6/5)9×7–4 (JD) 46974 ≈ 96/(47/4) (JD) 47332 ≈ 47×(3–(3–2)) (JD) 47395 ≈ 349/5–7 (JD) 47398 ≈ (9+(8×3)4)/7 (JD) 47671 ≈ (74/6+1)7 (JD) 47825 ≈ 82/(7+4)+5 (JD) 47852 ≈ (875/4)2 (JD) 48458 ≈ (8/54–4)8 (JD) 48724 ≈ ((8–4/7)×2)4 (JD) 48815 ≈ 58/8–14 (JD) 48825 ≈ (58+2)/8–4 (JD) 48829 ≈ ((9–4)8+2)/8 (JD) 48845 ≈ 58/8+4×4 (JD) 48857 ≈ 58/8+7×4 (JD) 49237 ≈ 793/4×2 (JD) 49272 ≈ 29(7–2)/4 (JD) 49343 ≈ (4×9)3+4–3 (JD) 49375 ≈ 39×(54/7) (JD) 49518 ≈ (8/5)9+14 (JD) 49592 ≈ (5/2)9×(9+4) (JD) 49659 ≈ 49–6/5–9 (JD) 49664 ≈ 669/4×4 (JD) 49675 ≈ 49/5+6+7 (JD) 51291 ≈ (9–(2–(1+1)))5 (JD) 51292 ≈ (9–(2–2))5+1 (JD) 51398 ≈ 59/38–1 (JD) 51399 ≈ 59/(39–1) (JD) 51643 ≈ (14/3)6×5 (JD) 52334 ≈ (2–3+5×3)4 (JD) 52339 ≈ 9(5/3)3×2 (JD) 52409 ≈ 49/5–20 (JD) 52427 ≈ (47+2)/5–2 (JD) 52429 ≈ 49/5+2–2 (JD) 52489 ≈ 94×8+2/5 (JD) 52735 ≈ (5/2+7×5)3 (JD) 52789 ≈ 8(97–2)×5 (JD) 52814 ≈ 158–2+4 (JD) 53454 ≈ 344/5/5 (JD) 53677 ≈ 76/(35/7) (JD) 53876 ≈ 3/(7–5–(8–6)) (JD) 53896 ≈ 368/9+5 (JD) 54297 ≈ 4279/5 (JD) 54694 ≈ 95/(64–4) (JD) 54763 ≈ (67–(3–4))/5 (JD) 55394 ≈ (9–4/35)5 (JD) 55472 ≈ (75+4)5/2 (JD) 55616 ≈ 66+5/51 (JD) 55784 ≈ 58/7–5×4 (JD) 55797 ≈ 59/7/5–7 (JD) 55798 ≈ (58–9×5)/7 (JD) 55837 ≈ 58/(7–(3–5)) (JD) 55976 ≈ (67–59)/5 (JD) 56786 ≈ ((7+6)6)/85 (JD) 57193 ≈ 95/(7–3+1) (JD) 57249 ≈ (9–4/72)5 (JD) 57358 ≈ ((8/5)7/3)5 (JD) 57838 ≈ 5883/7 (JD) 57892 ≈ –(5×(7–89/2)) (JD) 57938 ≈ (9/(78–3))5 (JD) 58231 ≈ (58–1/2)/3 (JD) 58329 ≈ (39+5)/82 (JD) 58416 ≈ 846/5–1 (JD) 58417 ≈ 84(7–1)/5 (JD) 58418 ≈ 884/5+1 (JD) 58425 ≈ (45–2–5)8 (JD) 58436 ≈ (4/(65–3))8 (JD) 58467 ≈ (58/6+7)4 (JD) 58539 ≈ (9–(83–5))5 (JD) 58667 ≈ 5–((8/6)–6–7) (JD) 58715 ≈ 8+(5–1/5)7 (JD) 58749 ≈ 95–74/8 (JD) 58794 ≈ (9–(4/8)7)5 (JD) 58921 ≈ (9–(1/2)8)5 (JD) 58923 ≈ 95–((8–3)/2) (JD) 58939 ≈ 958–(3–9) (JD) 58983 ≈ 85×9/(8–3) (JD) 58985 ≈ (9–(85–8))5 (JD) 58993 ≈ 95–83/9 (JD) 59047 ≈ (9–(40–7))5 (JD) 59048 ≈ 95–(40–8) (JD) 59049 ≈ 95–9/40 (JD) 59051 ≈ 95+10–5 (JD) 59052 ≈ 5/2+95+0 (JD) 59057 ≈ 50/7+95 (JD) 59073 ≈ 70/3+95 (JD) 59255 ≈ (9+(2–5)/5)5 (JD) 59260 ≈ 205/9/6 (JD) 59273 ≈ (9+(7–2)/3)5 (JD) 59279 ≈ 9(9–2)/7+5 (JD) 59281 ≈ 95/(1–(2–8)) (JD) 59297 ≈ (9+2–7)5–9 (JD) 59334 ≈ ((5–4+3)9)×3 (JD) 59337 ≈ (9+3/(73))5 (JD) 59347 ≈ 9(37–4)×5 (JD) 59364 ≈ 654/9×3 (JD) 59386 ≈ (96–3+8)5 (JD) 59464 ≈ 95×(64–4) (JD) 59629 ≈ 9(9+6)–2+5 (JD) 59721 ≈ (9+7–2)5–1 (JD) 59729 ≈ (9+2/97)5 (JD) 59745 ≈ 57–9/54 (JD) 59754 ≈ 9557–4 (JD) 59786 ≈ (5–9/8/6)7 (JD) 59788 ≈ 97/5/(8+8) (JD) 59825 ≈ (9+2/85)5 (JD) 61278 ≈ ((6+1/2)7)/8 (JD) 62734 ≈ (73/4+2)6 (JD) 62759 ≈ 96–2+5–7 (JD) 62775 ≈ (5–(2/(7+6)))7 (JD) 63148 ≈ ((6–3–1)×4)8 (JD) 64429 ≈ 944/6×2 (JD) 65327 ≈ –(6–(5–(3–2–7))) (JD) 65437 ≈ (5–3/6/4)7 (JD) 65438 ≈ ((6+5)–3–4)8 (JD) 65478 ≈ (7/(56)–4)8 (JD) 65485 ≈ (54–6–5)8 (JD) 65486 ≈ (6/(56)–4)8 (JD) 65528 ≈ 2/(85–6–5) (JD) 65538 ≈ (85×6+5)/3 (JD) 65548 ≈ 56/5+48 (JD) 65584 ≈ (5–5+4)8+6 (JD) 65612 ≈ (56/61)2 (JD) 65743 ≈ 76–(5–(3/4)) (JD) 65915 ≈ (9+1/5)5+6 (JD) 66429 ≈ (96/2–6)/4 (JD) 66469 ≈ 6(6/9)4+6 (JD) 66754 ≈ (5–4/6/6)7 (JD) 67052 ≈ 605/7+2 (JD) 67472 ≈ (67–(7–2))/4 (JD) 67474 ≈ 74/7×(6+4) (JD) 67543 ≈ 743/6+5 (JD) 67724 ≈ (6×4)7–7/2 (JD) 68441 ≈ (1/46+4)8 (JD) 68479 ≈ (96+47)/8 (JD) 69445 ≈ 56×(4/9+4) (JD) 69476 ≈ 647/9×6 (JD) 69754 ≈ (59/4–6)/7 (JD) 69985 ≈ 65×9+8/9 (JD) 71293 ≈ 137/2×9 (JD) 71541 ≈ (5–(4–(1+1)))7 (JD) 71542 ≈ (5–(4–2))7+1 (JD) 71842 ≈ 782–(1/4) (JD) 72358 ≈ 28/7+5×3 (JD) 72655 ≈ (6–(52–5))7 (JD) 72973 ≈ 723/79 (JD) 73143 ≈ ((34–1)3)/7 (JD) 73562 ≈ 27/6+5×3 (JD) 74121 ≈ (17–1/2)4 (JD) 74259 ≈ ((9+4)7–2)/5 (JD) 74358 ≈ ((5+3)/7)84 (JD) 74591 ≈ 79/541 (JD) 74650 ≈ ((7+5)6)/40 (JD) 74783 ≈ 4877–3 (JD) 74897 ≈ (87/7–9)/4 (JD) 75281 ≈ 827/5–1 (JD) 75282 ≈ 87/5+2+2 (JD) 75284 ≈ 87/5+4+2 (JD) 75426 ≈ 7+(5/2+4)6 (JD) 75628 ≈ 57/(82–6) (JD) 75629 ≈ (75×9–6)/2 (JD) 75632 ≈ 75×(6–3/2) (JD) 75916 ≈ 96/7–5×1 (JD) 75919 ≈ (95+1–9)/7 (JD) 75921 ≈ (95+2–1)/7 (JD) 75926 ≈ (96+2)/7+5 (JD) 75934 ≈ (3/5+9+7)4 (JD) 75936 ≈ 96/7+5×3 (JD) 76122 ≈ ((6–1/2)7)/2 (JD) 76347 ≈ 67×3/(7+4) (JD) 76438 ≈ (48/6–3)×7 (JD) 76458 ≈ (48×7–5)/6 (JD) 76589 ≈ 57–(96–8) (JD) 76752 ≈ (6–(52–7))7 (JD) 76853 ≈ (5–6/(83))7 (JD) 76945 ≈ 45+96/7 (JD) 77546 ≈ 57–(64–7) (JD) 77753 ≈ 57–(7–3)–7 (JD) 77894 ≈ 78/74–9 (JD) 78125 ≈ 57–8/21 (JD) 78126 ≈ 2/8+(6–1)7 (JD) 78145 ≈ 5(8+1)–4+7 (JD) 78235 ≈ ((8+2)–3+5)7 (JD) 78365 ≈ 58–3+7–6 (JD) 78633 ≈ (6–3+8–3)7 (JD) 78644 ≈ 6/(4–8+4–7) (JD) 78645 ≈ (48×6+7)/5 (JD) 78662 ≈ 6872/6 (JD) 78729 ≈ (7/2)9–87 (JD) 78816 ≈ (7/(8–6))8+1 (JD) 78842 ≈ 48+2/(8+7) (JD) 79328 ≈ 83+(7/2)9 (JD) 81597 ≈ (8/9–5)7+1 (JD) 81598 ≈ (8/9–5)8+1 (JD) 82155 ≈ 52–5+8–1 (JD) 82313 ≈ (81/2+3)3 (JD) 82569 ≈ 86–5/9–2 (JD) 83227 ≈ (72–2)8/3 (JD) 83655 ≈ 5583/6 (JD) 83679 ≈ 6(8/7)9+3 (JD) 83829 ≈ (9/2–3/8)8 (JD) 84273 ≈ 48×(37–2) (JD) 84279 ≈ 9×(48/7+2) (JD) 84357 ≈ (45–8/7)3 (JD) 84673 ≈ (843+6)/7 (JD) 85259 ≈ 852+5/9 (JD) 85334 ≈ (8×5)3/3×4 (JD) 85667 ≈ 586/7×6 (JD) 85741 ≈ (71/8+5)×4 (JD) 86579 ≈ 68×5/97 (JD) 86783 ≈ (8/7+3)8+6 (JD) 86785 ≈ 8+(6/7–5)8 (JD) 87381 ≈ 87/3/8–1 (JD) 87382 ≈ 87/(32–8) (JD) 87383 ≈ (87/8+3)/3 (JD) 87386 ≈ (86–8)/3+7 (JD) 87391 ≈ 9+(87–1)/3 (JD) 87462 ≈ 428/7+6 (JD) 87625 ≈ (62/8+7)/5 (JD) 87965 ≈ 95(8+7)/6 (JD) 88544 ≈ (8+8+5/4)4 (JD) 89664 ≈ (6–64/8)9 (JD) 91635 ≈ 96/5+3+1 (JD) 91645 ≈ (61/4)5/9 (JD) 92653 ≈ (9×(6–2+5))3 (JD) 92682 ≈ 89/6+2+2 (JD) 92684 ≈ 89/6+4+2 (JD) 92688 ≈ 89/2×8+6 (JD) 92867 ≈ –(((9–2)/8–6)7) (JD) 93423 ≈ (3+2)43/9 (JD) 93425 ≈ 543/9+2 (JD) 93784 ≈ 97/(8+43) (JD) 93943 ≈ (49+39)/3 (JD) 94532 ≈ (25/(4+3))9 (JD) 94537 ≈ (4/7+3)9+5 (JD) 94586 ≈ ((9+45)/8)6 (JD) 94774 ≈ 744/9×7 (JD) 94787 ≈ ((7/4)9+8)×7 (JD) 94817 ≈ 9184/7 (JD) 95537 ≈ (9–3)7/5+5 (JD) 96498 ≈ (9+69/8)4 (JD) 96825 ≈ (9/5–6)8–2 (JD) 96827 ≈ (9/(2–7)+6)8 (JD) 96945 ≈ (9–5×4/9)6 (JD) 97241 ≈ 214/(9–7) (JD) 97387 ≈ (9+7)3+8/7 (JD) 97439 ≈ (79/9)3/4 (JD) 97612 ≈ 97/((6+1)2) (JD) 97657 ≈ 59/(7+7+6) (JD) 98753 ≈ 5/(3–9–(7–8)) (JD) 98957 ≈ 9×(((9+7)/5)8) (JD)

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