n \ m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | |||||||||||||||||

2 | 1 | 1 | ||||||||||||||||

3 | 1 | 7/8 | 15/16 | |||||||||||||||

4 | 1 | 1 | 1 | 1 | ||||||||||||||

5 | 1 | .818+ (MM) | .917+ | 1 | 125/144 | |||||||||||||

6 | 1 | 8/9 | 1 | 1 | 67/72 | 68/75 | ||||||||||||

7 | 1 | 1 | 17/18 | 1 | .919+ (MM) | 17/18 | 35/36 | |||||||||||

8 | 1 | 1 | 35/36 | 1 | .963+ | .964+ (MM) | 1 | 1 | ||||||||||

9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||||||

10 | 1 | 29/32 | 187/196 | 1 | 15/16 | 1 | 47/49 (MM) | 48/49 | 1 | 449/490 (JD) | ||||||||

11 | 1 | 47/50 | .948+ | 1 | 1 | 49/50 | 73/75 | .977+ | 1 | 139/144 | .941+ (MM) | |||||||

12 | 1 | 59/64 (JD) | 24/25 | 1 | 237/256 (MM) | 1 | 139/144 (JD) | 120/121 | 1 | 23/24 | 383/400 | 24/25 | ||||||

13 | 1 | 15/16 | 1 | 1 | 137/144 | 379/400 (GS) | 115/121 | .979+ (BH) | 1 | 31/32 | 63/64 | 1 | 377/392 (MM) | |||||

14 | 1 | 1 | 31/32 | 1 | .954+ (MM) | 31/32 | 63/64 | 1 | 1 | 39/40 | 1 | 251/256 (JD) | 109/112 (MM) | .976+ (MM) | ||||

15 | 1 | 31/32 | 63/64 | 1 | .979+ | .979+ (MM) | 71/72 | 143/144 | 1 | 1 | .987+ (BH) | .987+ (BH) | .988+ (BH) | 127/128 | 255/256 | |||

16 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||

17 | 1 | 1 (JD) | .932+ (MM) | 1 | .934+ (MM) | 249/256 (MM) | 80/81 (MM) | 1 | 1 | 26/27 (MM) | 79/81 (MM) | 80/81 (MM) | 1 (MM) | 143/144 (MM) | .990+ (MM) | 1 | 221/225 | |

18 | 1 | 1 (JD) | 35/36 (MM) | 1 | 117/121 (JD) | 26/27 (MM) | 1 | 1 (MM) | 1 | 162/169 (MM) | 31/32 (MM) | 35/36 (MM) | 27/28 (MM) | 1 (MM) | 143/144 (MM) | 1 | 1 (MM) | 1 |

T(1) = 1 | T(2) = 1 | T(3) ≥ 15/16 |

T(4) = 1 | T(5) ≥ 125/144 | T(6) ≥ 68/75 |

T(7) ≥ 35/36 | T(8) = 1 | T(9) = 1 |

T(10) ≥ 449/490 (JD) | T(11) ≥ .941+ (MM) | T(12) ≥ 24/25 |

T(13) ≥ 377/392 (MM) | T(14) ≥ .976+ (MM) | T(15) ≥ 255/256 |

T(16) = 1 | T(17) ≥ 221/225 | T(18) = 1 |

T(19) ≥ 95/98 (MM) | T(20) = 1 | T(21) ≥ .978+ (MM) |

T(22) ≥ 286/289 (MM) | T(23) ≥ 1219/1225 (MM) | T(24) ≥ 624/625 (MM) |

If you can extend any of these results, please e-mail me. Click here to go back to Math Magic. Last updated 11/11/14.