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%I #24 Jun 18 2022 14:18:22
%S 3,3,9,3,3,9,3,3,27,3,3,9,3,3,9,3,3,27,3,3,9,3,3,9,3,3,81,3,3,9,3,3,9,
%T 3,3,27,3,3,9,3,3,9,3,3,27,3,3,9,3,3,9,3,3,81,3,3,9,3,3,9,3,3,27,3,3,
%U 9,3,3,9,3,3,27,3,3,9,3,3,9,3,3,243,3,3,9,3,3,9,3,3,27,3,3,9,3,3,9,3,3
%N Highest power of 3 dividing F(4n) where F(k) is the k-th Fibonacci number.
%C If m == 1, 2 or 3 (mod 4) then F(m) is not divisible by 3.
%H Amiram Eldar, <a href="/A074724/b074724.txt">Table of n, a(n) for n = 1..10000</a>
%F If k == 1 or 2 (mod 3) then a(3^m*k) = 3^(m+1) for m>=0.
%F a(n) = A038500(A033888(n)). - _Amiram Eldar_, May 13 2022
%F a(n) = 3^A051064(n) (conjectured). - _Michel Marcus_, May 17 2022
%F Conjecture: a(n) = (sigma(3*n) - sigma(n))/(sigma(3*n) - 3*sigma(n)), where sigma(n) = A000203(n). Equivalently, a(n) = A088838(n) - A074724(n). - _Peter Bala_, Jun 10 2022
%t Table[3^IntegerExponent[Fibonacci[4n],3],{n,100}] (* _Harvey P. Dale_, Jun 03 2012 *)
%o (PARI) a(n) = 3^valuation(fibonacci(4*n), 3); \\ _Michel Marcus_, May 13 2022
%Y Cf. A000045, A000203, A038500, A033888, A051064, A074724, A088838.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Sep 04 2002
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