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%I #20 Dec 29 2015 03:02:57
%S 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,
%T 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,
%U 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
%N a(n) is the exact power of 2 that divides the n-th Fibonacci number (A000045).
%H Robert Israel, <a href="/A060865/b060865.txt">Table of n, a(n) for n = 1..10000</a>
%F 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.
%F a(n) = F(n) / A174883(n). - _Franklin T. Adams-Watters_, Jan 24 2012
%F a(n) = A006519(A000045(n)). - _Michel Marcus_, Jul 30 2013
%F a(3n) = 2^A090740(n). - _Robert Israel_, Dec 28 2015
%e a(12) = 16 because the 12th Fibonacci number is 144 and 144 = 9*16.
%p seq(2^padic:-ordp(combinat:-fibonacci(n),2),n=1..100); # _Robert Israel_, Dec 28 2015
%o (PARI) a(n)=2^valuation(fibonacci(n), 2) \\_Michel Marcus_, Jul 30 2013
%Y Cf. A000045, A060904(n) = 5^A112765(n), A090740.
%K nonn,easy
%O 1,3
%A Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001
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