A175552 Numbers k such that the digit sum of 167^k is divisible by k.

1, 2, 5, 7, 22, 490, 724, 778, 868, 994, 1109, 1390, 1415, 1462, 1642, 1739, 1829, 2146, 2362, 3136, 4954, 6437, 6628, 7103, 11200, 12424, 12863, 14242, 14249, 15059, 15203, 16222, 17140, 18353, 19192, 21233, 22853, 24106, 24574, 24833, 26896, 27652, 28253, 30323, 31306, 31594, 32386, 33790, 34985, 36184, 36310, 40673, 42196, 43931, 45911, 45983

Offset

1,2

Comments

From Donovan Johnson, Dec 03 2010: (Start)

To generate the additional terms I used PFGW.exe to get the decimal expansion for each number of the form 167^n (n <= 50000). Then I wrote a program in powerbasic to read the pfgw.out file and get the digit sums.

The digit sum is 10 times the n value for terms a(5) to a(56). (End)

I believe that this sequence is finite. - N. J. A. Sloane, Dec 05 2010

Links

Donovan Johnson, Table of n, a(n) for n = 1..129

Mathematica

Select[Range[10000], Mod[Total[IntegerDigits[167^#]], #] == 0 &]

Crossrefs

Sum of digits of k^n mod n: (k=2) A000079, A001370, A175434, A175169; (k=3) A000244, A004166, A175435, A067862; (k=5) A000351, A066001, A175456; (k=6) A000400, A066002, A175457, A067864; (k=7) A000420, A066003, A175512, A067863; (k=8) A062933; (k=13) A001022, A175527, A175528, A175525; (k=21) A175589; (k=167) A175558, A175559, A175560, A175552.

Sequence in context: A158357 A072953 A243394 * A279756 A103060 A256247

Adjacent sequences: A175549 A175550 A175551 * A175553 A175554 A175555

Keyword

base,nonn

Author

N. J. A. Sloane, Dec 03 2010

Extensions

a(25)-a(56) from Donovan Johnson, Dec 03 2010

Status

approved