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%I #11 Jun 16 2018 16:14:08
%S 2,3,5,2,5,13,2,37,2,13,2,3,5,5,2,73,13,5,2,3,2,5,13,89,2,3,2,2,89,5,
%T 5,157,2,13,3,2,2,89,3,193,2,13,5,3,2,5,13,2,5,3,3,2,89,5,2,3,277,13,
%U 3,5,233,13,2,5,2,313,89,2,2,13,3,2,89,5,5,13,233,2,2,397,233,3,2,3,5
%N a(n) = gcd(n!, Fibonacci(n)) as n runs through A250444.
%C By the definition of A250444, all terms are prime.
%e For n = 9, GCD(9!, Fibonacci(9)) = 2, (prime, thus belongs to the sequence).
%t a[n_] := GCD[n!, Fibonacci[n]];
%t p[n_] := Which[PrimeQ[a[n]], a[n], PrimeQ[a[n]] == False, ];
%t Select[Table[p[n], {n, 1, 300}], IntegerQ[#] &]
%o (PARI) for(n=1,10^3,if(isprime(p=gcd(n!,fibonacci(n))),print1(p,", "))) \\ _Derek Orr_, Nov 23 2014
%Y Cf. A000045, A000142, A250444.
%K nonn,easy
%O 1,1
%A _Carlos Eduardo Olivieri_, Nov 23 2014
%E More terms from _Derek Orr_, Nov 23 2014
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