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repdigits

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(max 15 digits)

A number whose digits in a given base are all equal. more

The repdigits up to 1015 :
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999, 1111111, 2222222, 3333333, 4444444, 5555555, 6666666, 7777777, 8888888, 9999999, 11111111, 22222222, 33333333, 44444444, 55555555, 66666666, 77777777, 88888888, 99999999, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777, 888888888, 999999999, 1111111111, 2222222222, 3333333333, 4444444444, 5555555555, 6666666666, 7777777777, 8888888888, 9999999999, 11111111111, 22222222222, 33333333333, 44444444444, 55555555555, 66666666666, 77777777777, 88888888888, 99999999999, 111111111111, 222222222222, 333333333333, 444444444444, 555555555555, 666666666666, 777777777777, 888888888888, 999999999999, 1111111111111, 2222222222222, 3333333333333, 4444444444444, 5555555555555, 6666666666666, 7777777777777, 8888888888888, 9999999999999, 11111111111111, 22222222222222, 33333333333333, 44444444444444, 55555555555555, 66666666666666, 77777777777777, 88888888888888, 99999999999999, 111111111111111, 222222222222222, 333333333333333, 444444444444444, 555555555555555, 666666666666666, 777777777777777, 888888888888888, 999999999999999.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 90000 values, from 1 to 1010000).

n\r 0  1 
24000050000 2 
3499982000120001 3 
420000200012000029999 4 
51000020000200002000020000 5 
6199991000110001299991000010000 6 
723328116681166710001116671166810001 7 
81000010001100001000110000100001000019998 8 
9233326667666713333666766671333366676667 9 
10099991000110000100001000010000100001000010000 10 
11450005000500050005000500050005000500050000

A pictorial representation of the table above
motab
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.