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A129761

First differences of Fibbinary numbers (A003714).

1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 2, 1, 11, 1, 1, 2, 1, 3, 1, 1, 22, 1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 2, 1, 43, 1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 2, 1, 11, 1, 1, 2, 1, 3, 1, 1, 86, 1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 2, 1, 11, 1, 1, 2, 1, 3, 1, 1, 22, 1, 1, 2, 1, 3, 1, 1, 6, 1, 1, 2, 1, 171, 1, 1, 2, 1, 3, 1, 1, 6

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OFFSET

0,3

COMMENTS

Theorem: If the Zeckendorf representation of M ends with exactly k >= 0 zeros, ...10^k, then a(n) = ceiling(2^k/3). Also, if the Zeckendorf representation of n (A014417(n)) is even then a(n) is given by A319952, otherwise a(n) = 1. - Jeffrey Shallit and N. J. A. Sloane, Oct 03 2018

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..10000 (First 2500 terms from Vincenzo Librandi)

FORMULA

a(n) = A005578(A035614(n)). - Alan Michael Gómez Calderón, Nov 01 2023

MAPLE

with(combinat): F:=fibonacci:

A072649:= proc(n) local j; global F; for j from ilog[(1+sqrt(5))/2](n)

while F(j+1)<=n do od; (j-1); end:

A003714 := proc(n) global F; option remember; if(n < 3) then RETURN(n); else RETURN((2^(A072649(n)-1))+A003714(n-F(1+A072649(n)))); fi; end:

A129761 := n -> A003714(n+1)-A003714(n):

[seq(A129761(n), n=0..120)]; # N. J. A. Sloane, Oct 03 2018, borrowing programs from other sequences

MATHEMATICA