A287058 Sum of decimal digits of 118^n.

1, 10, 19, 19, 55, 64, 55, 64, 82, 91, 109, 100, 109, 181, 118, 145, 127, 163, 154, 172, 154, 190, 226, 190, 208, 217, 271, 289, 253, 280, 298, 307, 334, 289, 334, 280, 361, 343, 334, 379, 406, 406, 379, 424, 379, 424, 415, 406, 523, 433, 478

Offset

0,2

Comments

118 is exceptional in the sense that it appears to be the only number m for which the smallest k such that sumdigits(m^k) = m occurs after the smallest k such that sumdigits(m^k) > m*3/2. If this last limit is decreased to m*4/3, then 31 and 86 also have this property. It appears that no number has this property if the limit is increased to 2m, see also A247889.

It is also remarkable that many values in the sequence are repeated (19, 55, 64, 109, 190, 154, 280, 289, 334 (3 times), 379, 406, 424, ...), while most other numbers never appear.

Links

Table of n, a(n) for n=0..50.

Mathematica

Total[IntegerDigits[#]]&/@NestList[118#&, 1, 50] (* Harvey P. Dale, Feb 24 2022 *)

Prog

(PARI) a(n)=sumdigits(118^n)

Crossrefs

Cf. A007953, A247889.

Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), A065713 (k=4), A066001(k=5), A066002 (k=6), A066003 (k=7), A066004 (k=8), A065999 (k=9), A066005 (k=11), A066006 (k=12).

Sequence in context: A122607 A113703 A103757 * A061016 A038366 A210539

Adjacent sequences: A287055 A287056 A287057 * A287059 A287060 A287061

Keyword

nonn,base

Author

M. F. Hasler, May 18 2017

Status

approved