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Primes of the form f^2-2, where f is a Fibonacci number.
1

%I #3 Mar 31 2012 12:38:25

%S 2,7,23,167,439,3023,7919,54287,974167,2550407,32522920134767,

%T 3372041405099481407,9839618880490124200692486211717007,

%U 724995932728680612729658820311719934835368079

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

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

%C 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, ...

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

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

%Y Cf. A000045, A028871

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009

%E Comments from _Charles R Greathouse IV_, Nov 09 2009