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Numbers n such that gcd(n!, Fibonacci(n)) is prime.
2

%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