

A175525


Numbers n such that n divides the sum of digits of 13^n.


9



1, 2, 5, 140, 158, 428, 788, 887, 914, 1814, 1895, 1976, 2579, 2732, 3074, 3299, 3641, 4658, 4874, 5378, 5423, 5504, 6170, 6440, 6944, 8060, 8249, 8915, 9041, 9158, 9725, 9824, 10661, 11291, 13820, 15305, 17051, 17393, 18716, 19589, 20876, 21641, 23756, 24188, 25961, 28409, 30632, 31307, 32387, 33215, 34970, 35240, 36653, 36977, 41558, 43970, 44951, 47444, 51764, 52655, 53375, 53852, 54104, 56831, 57506, 59153, 66479, 68063, 73562, 78485, 79286, 87908, 92093, 102029, 106934, 114854, 116321, 134051, 139397, 184037, 192353, 256469, 281381, 301118, 469004
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OFFSET

1,2


COMMENTS

Almost certainly there are no further terms.
Comments from Donovan Johnson on the computation of this sequence, Dec 05 2010 (Start):
The number of digits of 13^n is approximately 1.114*n, so I defined an array d() that is a little bigger than 1.114 times the maximum n value to be checked. The elements of d() each are the value of a single digit of the decimal expansion of 13^n with d(1) being the least significant digit.
It's easier to see how the program works if I start with n = 2.
For n = 1, d(2) would have been set to 1 and d(1) would have been set to 3.
n = 2:
x = 13*d(1) = 13*3 = 39
y = 39\10 = 3 (integer division)
xy*10 = 3930 = 9, d(1) is set to 9
x = 13*d(2)+y = 13*1+3 = 16, y is the carry from previous digit
y = 16\10 = 1
xy*10 = 1610 = 6, d(2) is set to 6
x = 13*d(3)+y = 13*0+1 = 1, y is the carry from previous digit
y = 1\10 = 0
xy*10 = 10 = 1, d(3) is set to 1
These steps would of course be inside a loop and that loop would be inside an n loop. A pointer to the most significant digit increases usually by one and sometimes by two for each successive n value checked. The number of steps of the inner loop is the size of the pointer. A scan is done from the first element to the pointer element to get the digit sum.
(End)
No other terms < 3*10^6.  Donovan Johnson


LINKS

Table of n, a(n) for n=1..85.


MATHEMATICA

Select[Range[1000], Mod[Total[IntegerDigits[13^#]], #] == 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: A183128 A145620 A130412 * A069139 A155762 A307480
Adjacent sequences: A175522 A175523 A175524 * A175526 A175527 A175528


KEYWORD

nonn,base


AUTHOR

T. D. Noe, Dec 03 2010


EXTENSIONS

a(47)a(79) from N. J. A. Sloane, Dec 04 2010
a(80)a(85) from Donovan Johnson, Dec 05 2010


STATUS

approved



