A059016 Number of 0's in binary expansion of Fibonacci(n).

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, 13, 9, 11, 13, 12, 11, 16, 14, 11, 11, 14, 13, 12, 16, 10, 19, 21, 15, 16, 18, 18, 19, 21, 16, 17, 23, 16, 20, 25, 23, 16, 20, 24, 19, 26, 20, 32, 24, 25, 27, 24, 23, 27, 28, 29, 31

Offset: 0

Author

Patrick De Geest, Jan 15 2001

Keywords

• nonn
• base

Comments

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A011373.

Programs

Maple

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

PARI

a(n)={ my(k=fibonacci(n)); if (k==0, 1, #select(x->!x,  binary(k)))} \\ Harry J. Smith, Jun 24 2009

Formula

a(n) = A023416(A000045(n)). - R. J. Mathar, Nov 05 2012