A095792 a(n) = Z(n) - L(n), where Z=A072649 and L=A095791 are lengths of Zeckendorf and lazy Fibonacci representations in binary notation.

0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n)=0 if n is of the form F(k)-1 for k>=1 and a(n)=1 otherwise.

Example

Zeckendorf-binary of 11 is 10100; lazy-Fibonacci-binary of 11 is 1111.
Thus Z(11)=5, L(11)=4 and a(11)=5-4=1.

Mathematica

t1 = DeleteCases[IntegerDigits[-1 + Range[5001], 2], {___, 0, 0, ___}]; (* maximal, lazy *)
t2 = DeleteCases[IntegerDigits[-1 + Range[5001], 2], {___, 1, 1, ___}];  (* minimal, Zeckendorf *)
m = Map[Length, t2] - Take[Map[Length, t1], Length[t2]] (* A095792 *)
(* Peter J. C. Moses, Mar 03 2015 *)

Crossrefs

Cf. A000045, A072649, A095791.

Sequence in context: A252742 A066247 A151774 * A288381 A169675 A093385

Adjacent sequences: A095789 A095790 A095791 * A095793 A095794 A095795

Keyword

nonn

Author

Clark Kimberling, Jun 05 2004

Status

approved