A117592 a(n) = a(3n) = a(3n+1) = a(3n+2)/2 with a(0)=1.

1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 8, 1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 8, 2, 2, 4, 2, 2, 4, 4, 4, 8, 2, 2, 4, 2, 2, 4, 4, 4

Offset: 0

Author

Paul Barry, Apr 05 2006

Keywords

• nonn
• base

Comments

Row sums of number triangle A117944.

Product of the nonzero digits of (n written in base 3). - Ilya Gutkovskiy, Nov 15 2020

a(n) = 1, 2, 4, 8, 16, 32, 64 iff n is respectively in A005836, A023699, A023700, A023701, A023702, A023703, A023704. - Bernard Schott, Dec 04 2020

Links

• Felix Fröhlich, Table of n, a(n) for n = 0..10000 (first 2001 terms from Vincenzo Librandi)

Crossrefs

See A338882 for similar sequences.

Cf. A081603 (log_2), A117942 (signed), A117944.

Cf. A005836, A023699, A023700, A023701, A023702, A023703, A023704.

Programs

Mathematica

Nest[ Join[#, #, 2#] &, {1}, 5] (* Robert G. Wilson v, Jul 27 2014 *)

PARI

a(n) = 1 << hammingweight(digits(n,3)>>1); \\ Kevin Ryde, Nov 15 2020

Python

from gmpy2 import digits
def A117592(n): return 1<Chai Wah Wu, Dec 05 2024

Formula

a(n) = a(3n)/a(0) = a(3n+1)/a(1) = a(3n+2)/a(2).

a(n) = abs(A117942(n)).

G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2) * A(x^3). - Ilya Gutkovskiy, Nov 15 2020

a(n) = 2^A081603(n). - Kevin Ryde, Nov 15 2020

Extensions

a(0) = 1 added to the Name by Bernard Schott, Dec 04 2020