A066001 Sum of digits of 5^n.

1, 5, 7, 8, 13, 11, 19, 23, 25, 26, 40, 38, 28, 23, 34, 44, 58, 56, 64, 59, 61, 62, 67, 74, 82, 77, 79, 89, 85, 83, 91, 104, 106, 89, 103, 92, 109, 104, 124, 134, 130, 137, 145, 149, 151, 116, 112, 128, 145, 158, 151, 152, 130, 119, 127, 167, 196, 215, 211, 191

Offset: 0

Author

N. J. A. Sloane, Dec 11 2001

Keywords

• nonn
• base

Comments

We can expect and conjecture that a(n) ~ 4.5*log_10(5)*n, but for n ~ 10^3..10^4 there are still fluctuations of +- 1%, e.g., a(10^3)/log_10(5) ~ 4538, a(10^4)/log_10(5) ~ 44518. Modulo 9, the sequence is periodic with period (1, 5, 7, 8, 4, 2) of length 6. No term is divisible by 3, a(n) = (-1)^n (mod 3). - M. F. Hasler, May 18 2017

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007953, A000351.

Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), A065713 (k=4), this sequence (k=5), A066002 (k=6), A066003 (k=7), A066004 (k=8), A065999 (k=9), A066005 (k=11), A066006 (k=12), A175527 (k=13).

Programs

Mathematica

Table[ Total@ IntegerDigits[5^n], {n, 0, 60}] (* Robert G. Wilson v, Oct 25 2006 *)
Table[Total[IntegerDigits[5^n]], {n, 0, 60}] (* Vincenzo Librandi, Oct 08 2013 *)

PARI

a(n)=sumdigits(5^n); \\ Michel Marcus, Sep 04 2014

Formula

a(n) = A007953(A000351(n)). - Michel Marcus, Aug 05 2025