A290864 Numbers k such that the k-th Fibonacci polynomial evaluated at k is prime.

2, 5, 71, 8419

Offset: 1

Author

Bobby Jacobs, Aug 12 2017

Keywords

• nonn
• more
• hard

Comments

Numbers k such that A084844(k) = A117715(k,k) is prime.

a(5) > 9200. - Giovanni Resta, Aug 13 2017

Except for a(1), all terms == 1 or 5 (mod 6). - Robert Israel, Aug 13 2017

Examples

			5 is in the sequence because A117715(5,5) = 701 is prime.
		

Links

• Eric Weisstein's World of Mathematics, Fibonacci Polynomial
• Wikipedia, Fibonacci polynomials

Crossrefs

Cf. A000045, A011973, A084844, A117715, A162515, A168561.

Programs

Maple

select(t -> isprime(combinat:-fibonacci(t,t)), [2,seq(seq(6*i+j,j=[1,5]),i=0..100)]); # Robert Israel, Aug 13 2017

Mathematica

Select[Range[100], PrimeQ@ Fibonacci[#, #] &] (* Giovanni Resta, Aug 13 2017 *)

Extensions

a(4) from Giovanni Resta, Aug 13 2017