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A129761 First differences of Fibbinary numbers (A003714). 5
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 (list; graph; refs; listen; history; text; internal format)
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)

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, A319432.

Sequence in context: A178534 A110619 A191861 * A319299 A207031 A156248

Adjacent sequences:  A129758 A129759 A129760 * A129762 A129763 A129764

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 14 2007

EXTENSIONS

Added a(0)=1. - N. J. A. Sloane, Oct 02 2018

STATUS

approved

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Last modified October 18 14:05 EDT 2018. Contains 316321 sequences. (Running on oeis4.)