A250445 a(n) = gcd(n!, Fibonacci(n)) as n runs through A250444.

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, 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, 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

Offset: 1

Author

Carlos Eduardo Olivieri, Nov 23 2014

Keywords

• nonn
• easy

Comments

By the definition of A250444, all terms are prime.

Examples

			For n = 9, GCD(9!, Fibonacci(9)) = 2, (prime, thus belongs to the sequence).
		

Crossrefs

Cf. A000045, A000142, A250444.

Programs

Mathematica

a[n_] := GCD[n!, Fibonacci[n]];
p[n_] := Which[PrimeQ[a[n]], a[n], PrimeQ[a[n]] == False, ];
Select[Table[p[n], {n, 1, 300}], IntegerQ[#] &]

PARI

for(n=1,10^3,if(isprime(p=gcd(n!,fibonacci(n))),print1(p,", "))) \\ Derek Orr, Nov 23 2014

Extensions

More terms from Derek Orr, Nov 23 2014