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

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

Differences[Select[Range[600], !MemberQ[Partition[IntegerDigits[#, 2], 2, 1], {1, 1}] &]] (* Harvey P. Dale, Jul 17 2011 *)

Crossrefs

Cf. A000045, A000071, A003714, A005578, A035614, A319432.

Sequence in context: A354234 A191861 A350200 * A319299 A207031 A156248

Adjacent sequences: A129758 A129759 A129760 * A129762 A129763 A129764

Keyword

nonn

Author

Ralf Stephan, May 14 2007

Extensions

a(0)=1 added by N. J. A. Sloane, Oct 02 2018

Status

approved