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

Author

M. F. Hasler, May 18 2017

Keywords

• nonn
• base

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.

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).

Programs

Mathematica

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

PARI

a(n)=sumdigits(118^n)