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

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Keywords

• nonn

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, ...

Examples

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

Crossrefs

Cf. A000045, A028871

Programs

Mathematica

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

Extensions

Comments from Charles R Greathouse IV, Nov 09 2009