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

Author

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

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

Table[2^IntegerExponent[Fibonacci[n],2],{n,100}] (* Harvey P. Dale, Aug 04 2025 *)

PARI

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

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

Extensions

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