A118737 Number of zeros in binary expansion of 5^n.

0, 1, 2, 1, 5, 6, 7, 9, 7, 8, 13, 11, 15, 17, 16, 15, 18, 20, 18, 26, 21, 20, 27, 27, 26, 40, 30, 30, 37, 32, 33, 39, 36, 43, 37, 42, 40, 44, 51, 45, 40, 42, 49, 48, 51, 52, 57, 61, 58, 54, 59, 59, 67, 60, 68, 54, 70, 66, 61, 72, 79, 65, 70, 66, 63, 73, 67, 71, 76, 72, 80, 86, 78

Offset: 0

Author

Zak Seidov, May 22 2006

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000351, A023416, A061785, A118738.

Programs

Maple

seq(numboccur(0,convert(5^n,base,2)),n=0..100); # Robert Israel, Dec 24 2017

Mathematica

a[n_] := DigitCount[5^n, 2, 0]; Table[a[n], {n, 0, 72}] (* Ray Chandler, Sep 29 2006 *)
DigitCount[5^Range[0,80],2,0] (* Harvey P. Dale, Aug 30 2021 *)

PARI

a(n) = #binary(5^n)-hammingweight(5^n) \\ Felix Fröhlich, Dec 24 2017

Formula

a(n) + A118738(n) = A061785(n)+1 for n >= 1. - Robert Israel, Dec 24 2017

a(n) = A023416(A000351(n)). - Felix Fröhlich, Dec 24 2017