A061393 Number of appearances of n in sequence defined by b(k) = b(floor(k/3)) + b(ceiling(k/3)) with b(0)=0 and b(1)=1, i.e., in A061392.

1, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2, 10, 2, 4, 2, 82, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2, 10, 2, 4, 2, 244, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2, 10, 2, 4, 2, 82, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2, 10, 2, 4, 2, 730, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2, 10, 2, 4, 2, 82, 2, 4, 2, 10, 2, 4, 2, 28, 2, 4, 2

Offset: 0

Author

Henry Bottomley, Apr 30 2001

Keywords

• nonn

Comments

In the binary expansion of n, delete everything left of the rightmost 1 bit, then interpret as ternary and add 1. - Ralf Stephan, Aug 22 2013

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Michael Gilleland, Some Self-Similar Integer Sequences
• R. Stephan, Some divide-and-conquer sequences ...
• R. Stephan, Table of generating functions
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A061392.

Programs

PARI

A061393(n) = if(!n,1,(1+3^valuation(n,2))); \\ Antti Karttunen, Sep 30 2018

Formula

a(n) = A034472(A007814(n)) for n > 0.

a(2n) = 3a(n)-2; a(2n+1) = 2.

G.f.: 1/(1-x) + Sum_{k>=0} 3^k*x^2^k/(1 - x^2^(k+1)). - Ralf Stephan, Jun 13 2003