The repfigit numbers up to 1015 :
14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604, 62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993, 1084051, 7913837, 11436171, 33445755, 44121607, 129572008, 251133297, 24769286411, 96189170155, 171570159070, 202366307758, 239143607789, 296658839738, 1934197506555, 8756963649152, 43520999798747, 74596893730427, 97295849958669, 120984833091531, 270585509032586, 754788753590897.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 94 values, from 14 to 7⋅1028).
| n\r | 0 | 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 52 | 42 | 2 | ||||||||
| 3 | 27 | 36 | 31 | 3 | |||||||
| 4 | 28 | 20 | 24 | 22 | 4 | ||||||
| 5 | 19 | 16 | 20 | 17 | 22 | 5 | |||||
| 6 | 16 | 16 | 16 | 11 | 20 | 15 | 6 | ||||
| 7 | 15 | 9 | 18 | 10 | 11 | 17 | 14 | 7 | |||
| 8 | 17 | 10 | 11 | 16 | 11 | 10 | 13 | 6 | 8 | ||
| 9 | 8 | 13 | 14 | 7 | 14 | 10 | 12 | 9 | 7 | 9 | |
| 10 | 10 | 8 | 8 | 6 | 15 | 9 | 8 | 12 | 11 | 7 | 10 |
| 11 | 8 | 6 | 13 | 7 | 6 | 8 | 10 | 2 | 6 | 14 | 14 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.
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