%I #11 Nov 28 2014 23:31:28
%S 3,4,5,9,10,14,33,38,39,49,51,52,55,65,69,74,77,85,87,92,93,115,119,
%T 121,123,124,129,141,143,145,155,158,159,161,172,177,183,187,188,194,
%U 201,203,205,212,213,215,217,219,235,236,244,249,253,265,267,268,278,287,292,295,299
%N Numbers n such that gcd(n!, Fibonacci(n)) is prime.
%H Robert Israel, <a href="/A250444/b250444.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 3: GCD(3!, Fibonacci(3)) = 2.
%e For n = 4: GCD(4!, Fibonacci(4)) = 3.
%e For n = 9: GCD(9!, Fibonacci(9)) = 2.
%p select(n -> isprime(igcd(n!, combinat:-fibonacci(n))), [$1..1000]); # _Robert Israel_, Nov 24 2014
%t Select[Range[300], PrimeQ[GCD[#!, Fibonacci[#]] ] &]
%o (PARI) for(n=1,10^3,if(isprime(gcd(n!,fibonacci(n))),print1(n,", "))) \\ _Derek Orr_, Nov 23 2014
%K nonn,easy
%O 1,1
%A _Carlos Eduardo Olivieri_, Nov 23 2014