A118736 Number of zeros in binary expansion of 3^n.

0, 0, 2, 1, 4, 2, 4, 7, 7, 7, 7, 5, 10, 10, 9, 9, 15, 13, 15, 14, 15, 14, 16, 15, 23, 22, 18, 13, 20, 21, 23, 24, 25, 19, 25, 24, 31, 25, 25, 30, 36, 26, 29, 30, 36, 38, 28, 37, 36, 45, 39, 35, 41, 50, 47, 46, 50, 51, 50, 46, 40, 41, 50, 43, 46, 53, 60, 60, 53, 55, 47, 45, 57, 58

Offset

0,3

Links

Johann Peters, Table of n, a(n) for n = 0..10000

Taylor Dupuy and David E. Weirich, Bits of 3^n in binary, Wieferich primes and a conjecture of Erdős, Journal of Number Theory, Volume 158, January 2016, Pages 268-280.

Mathematica

f[n_] := DigitCount[3^n, 2, 0]; Table[f[n], {n, 0, 73}] (* Ray Chandler, Sep 29 2006 *)

Prog

(PARI) a(n) = #select(x->(x==0), binary(3^n)); \\ Michel Marcus, Apr 14 2020
(Python)
def A118736(n): return (m:=3**n).bit_length()-m.bit_count() # Chai Wah Wu, May 07 2026

Crossrefs

Cf. A011754 (number of ones in binary expansion of 3^n).

Sequence in context: A233521 A035685 A205509 * A201161 A216568 A219432

Adjacent sequences: A118733 A118734 A118735 * A118737 A118738 A118739

Keyword

base,nonn

Author

Zak Seidov, May 22 2006

Status

approved