1,1

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, ...

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

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

Cf. A000045, A028871

Sequence in context: A002494 A032264 A139522 this_sequence A112089 A075062 A022497

Adjacent sequences: A163155 A163156 A163157 this_sequence A163159 A163160 A163161

nonn,new

Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 21 2009

Comments from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 09 2009