A104320 Number of zeros in ternary representation of 2^n.

0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 0, 4, 2, 3, 3, 3, 3, 3, 7, 7, 9, 5, 6, 6, 4, 4, 3, 5, 6, 7, 9, 9, 10, 6, 6, 9, 9, 8, 9, 8, 7, 13, 12, 13, 9, 5, 9, 8, 6, 16, 13, 9, 10, 11, 11, 7, 14, 13, 13, 9, 12, 14, 15, 15, 11, 11, 17, 15, 19, 14, 19, 12, 18, 15, 11, 10, 16, 15, 14, 14, 13, 17, 14

Offset: 0

Author

Reinhard Zumkeller, Mar 01 2005

Keywords

• nonn
• base

Comments

Conjecture from N. J. A. Sloane: a(n) > 0 for n > 15, see A102483.

Examples

			n=13: 2^13=8192 -> '102020102', a(13) = 4.
		

Links

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

Crossrefs

Cf. A004642, A007089.

Programs

Magma

[Multiplicity(Intseq(2^n,3),0):n in [0..90]]; // Marius A. Burtea, Nov 17 2019

Maple

f:= n -> numboccur(0, convert(2^n,base,3)):
map(f, [$0..100]); # Robert Israel, Nov 17 2019

Mathematica

Table[DigitCount[2^n,3,0],{n,0,90}] (* Harvey P. Dale, May 06 2014 *)

PARI

a(n) = my(d=vecsort(digits(2^n, 3))); #setintersect(d, vector(#d)) \\ Felix Fröhlich, Nov 17 2019

PARI

a(n) = #select(d->!d, digits(2^n, 3)); \\ Ruud H.G. van Tol, May 09 2024

Formula

a(n) = A077267(A000079(n)).

a(A104321(n))=n and a(m)<>n for m < A104321(n).