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

2, 5, 71, 8419

Offset

1,1

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

Links

Table of n, a(n) for n=1..4.

Eric Weisstein's World of Mathematics, Fibonacci Polynomial

Wikipedia, Fibonacci polynomials

Example

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

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 *)

Crossrefs

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

Sequence in context: A100009 A167218 A013045 * A309366 A007506 A042693

Adjacent sequences: A290861 A290862 A290863 * A290865 A290866 A290867

Keyword

nonn,more

Author

Bobby Jacobs, Aug 12 2017

Extensions

a(4) from Giovanni Resta, Aug 13 2017

Status

approved