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a(n) = Z(n) - L(n), where Z=A072649 and L=A095791 are lengths of Zeckendorf and lazy Fibonacci representations in binary notation.
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%I #13 Oct 19 2019 15:19:39

%S 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,

%T 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,

%U 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

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

%H Amiram Eldar, <a href="/A095792/b095792.txt">Table of n, a(n) for n = 0..10000</a>

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

%e Zeckendorf-binary of 11 is 10100; lazy-Fibonacci-binary of 11 is 1111.

%e Thus Z(11)=5, L(11)=4 and a(11)=5-4=1.

%t t1 = DeleteCases[IntegerDigits[-1 + Range[5001], 2], {___, 0, 0, ___}]; (* maximal, lazy *)

%t t2 = DeleteCases[IntegerDigits[-1 + Range[5001], 2], {___, 1, 1, ___}]; (* minimal, Zeckendorf *)

%t m = Map[Length, t2] - Take[Map[Length, t1], Length[t2]] (* A095792 *)

%t (* _Peter J. C. Moses_, Mar 03 2015 *)

%Y Cf. A000045, A072649, A095791.

%K nonn

%O 0,1

%A _Clark Kimberling_, Jun 05 2004