A163158 Primes of the form f^2-2, where f is a Fibonacci number.

2, 7, 23, 167, 439, 3023, 7919, 54287, 974167, 2550407, 32522920134767, 3372041405099481407, 9839618880490124200692486211717007, 724995932728680612729658820311719934835368079

Offset

1,1

Comments

A basic heuristic suggests that this sequence is infinite with about k * log_phi(n) members below n.

Indices of associated Fibonacci numbers are 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 34, 46, 83, 109, 113, 158, 181, 203, 350, 490, 491, 565, 1024, 1114, 2800, 4222, 4847, 4961, 11507, 12554, ...

Links

Table of n, a(n) for n=1..14.

Example

2^2-2=2, 3^2-2=7, 5^2-2=23

Mathematica

f[n_]:=Fibonacci[n]^2-2; lst={}; Do[If[PrimeQ[f[n]], AppendTo[lst, f[n]]], {n, 6!}]; lst

Crossrefs

Cf. A000045, A028871

Sequence in context: A002494 A032264 A139522 * A355981 A171130 A112089

Adjacent sequences: A163155 A163156 A163157 * A163159 A163160 A163161

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Extensions

Comments from Charles R Greathouse IV, Nov 09 2009

Status

approved