A060865 a(n) is the exact power of 2 that divides the n-th Fibonacci number (A000045).

1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 64, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 128, 1, 1, 2, 1

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

If n is not divisible by 3 then a(n) = 1, if n = 3 * 2^k * (2m + 1) then a(n) = 2 if k=0 or 2^(k+2) if k>0.

a(n) = F(n) / A174883(n). - Franklin T. Adams-Watters, Jan 24 2012

a(n) = A006519(A000045(n)). - Michel Marcus, Jul 30 2013

a(3n) = 2^A090740(n). - Robert Israel, Dec 28 2015

Example

a(12) = 16 because the 12th Fibonacci number is 144 and 144 = 9*16.

Maple

seq(2^padic:-ordp(combinat:-fibonacci(n), 2), n=1..100); # Robert Israel, Dec 28 2015

Prog

(PARI) a(n)=2^valuation(fibonacci(n), 2) \\Michel Marcus, Jul 30 2013

Crossrefs

Cf. A000045, A060904(n) = 5^A112765(n), A090740.

Sequence in context: A007375 A294808 A294605 * A078689 A230069 A276813

Adjacent sequences: A060862 A060863 A060864 * A060866 A060867 A060868

Keyword

nonn,easy

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001

Status

approved