A163159 Fibonacci numbers F such that F^2-2 is prime.

2, 3, 5, 13, 21, 55, 89, 233, 987, 1597, 5702887, 1836311903, 99194853094755497, 26925748508234281076009, 184551825793033096366333, 468340976726457153752543329995929, 30010821454963453907530667147829489881, 1188518561323126046432205871807859915657177

Offset

1,1

Comments

In condensed representation: The A000045(i) at i = 3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 34, 46,... [R. J. Mathar, Jul 25 2009]

Links

Table of n, a(n) for n=1..18.

Formula

{A000045(i): A008865(A000045(i)) in A000040}. [R. J. Mathar, Jul 25 2009]

Example

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

Mathematica

f[n_]:=Fibonacci[n]; f2[n_]:=f[n]^2-2; lst={}; Do[If[PrimeQ[f2[n]], AppendTo[lst, f[n]]], {n, 6!}]; lst
Select[Fibonacci[Range[400]], PrimeQ[#^2-2]&] (* Harvey P. Dale, Oct 21 2011 *)

Crossrefs

Cf. A000045, A028871, A163158

Sequence in context: A061305 A177374 A142881 * A048736 A235621 A193300

Adjacent sequences: A163156 A163157 A163158 * A163160 A163161 A163162

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Extensions

More terms from Harvey P. Dale, Oct 21 2011

Status

approved