A065713 Sum of digits of 4^n.

1, 4, 7, 10, 13, 7, 19, 22, 25, 19, 31, 25, 37, 40, 43, 37, 58, 61, 64, 67, 61, 46, 58, 70, 73, 76, 79, 82, 85, 70, 82, 85, 88, 109, 103, 70, 109, 130, 106, 100, 112, 124, 118, 112, 115, 118, 139, 151, 127, 112, 115, 118, 121, 142, 145, 121, 160

Offset: 0

Author

N. J. A. Sloane, Dec 11 2001

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A000302, A007953.

Cf. sum of digits of k^n: A001370 (k=2), A004166 (k=3), this sequence (k=4), A066001 (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[4^n]], {n, 0, 60}] (* Vincenzo Librandi, Oct 08 2013 *)

PARI

a065713(n)=sumdigits(4^n); \\ Michel Marcus, Nov 01 2013

Formula

a(n) = A007953(A000302(n)). - Michel Marcus, Nov 01 2013 [corrected by Georg Fischer, Dec 19 2020]

a(n) = A001370(2n). Results given there imply a(n) > log_4(n) + 1/2, n > 0, but we can conjecture & expect a(n) ~ 9*log_10(2)*n. - M. F. Hasler, May 18 2017