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Number of 0's in binary expansion of Fibonacci(n).
3

%I #18 Aug 11 2017 03:30:57

%S 1,0,0,1,0,1,3,1,2,4,1,3,6,3,3,6,2,4,8,8,5,8,7,4,10,11,8,7,8,7,12,10,

%T 13,9,11,13,12,11,16,14,11,11,14,13,12,16,10,19,21,15,16,18,18,19,21,

%U 16,17,23,16,20,25,23,16,20,24,19,26,20,32,24,25,27,24,23,27,28,29,31

%N Number of 0's in binary expansion of Fibonacci(n).

%C Records are 1, 3, 4, 6, 8, 10, 11, 12, 13, 16, 19, 21, 23, 25, 26, 32, ... at positions 0, 6, 9, 12, 18, 24, 25, 30, 32, 38, 47, 48, 57, ... - _R. J. Mathar_, Nov 05 2012

%H T. D. Noe, <a href="/A059016/b059016.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A023416(A000045(n)). - _R. J. Mathar_, Nov 05 2012

%p with(combinat): a := proc (n) local fbin: fbin := convert(fibonacci(n), base, 2): nops(fbin)-add(fbin[j], j = 1 .. nops(fbin)) end proc: seq(a(n), n = 0 .. 80); # _Emeric Deutsch_, Jul 09 2009

%o (PARI) b(n)= { if (n==0, return(1)); c=0; i=n; until (i<=1, q=i/2; if (frac(q)==0, c++); i=floor(q); ); return (c); } { for (n = 0, 1000, a=b(fibonacci(n)); write("b059016.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jun 24 2009

%Y Cf. A011373.

%K nonn,base

%O 0,7

%A _Patrick De Geest_, Jan 15 2001