A095792 - OEIS

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

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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 *)