A051694 -id:A051694 - cp's OEIS frontend

A117517 Numbers k such that F(2*k + 1) is prime where F(m) is a Fibonacci number.

1, 2, 3, 5, 6, 8, 11, 14, 21, 23, 41, 65, 68, 179, 215, 216, 224, 254, 284, 285, 1485, 2361, 2693, 4655, 4838, 7215, 12780, 15378, 17999, 18755, 25416, 40919, 52455, 65010, 74045, 100553, 198689, 216890, 295020, 296844, 302355, 465758, 524948, 642803, 818003, 901529, 984360, 1452176

Offset: 1

Parthasarathy Nambi, Apr 26 2006

nonn

For F(k) to be prime, with k > 4, it is necessary but not sufficient for k to be prime. Hence after F(4) = 3, every prime F(m) is of the form F(2*k+1) for some k. Every prime divides some Fibonacci number. See also comment to A093062. - Jonathan Vos Post, Apr 29 2006

			If k=68 then F(2*k + 1) = 19134702400093278081449423917, a prime, so 68 is a term.

H. Dubner and W. Keller, New Fibonacci and Lucas Primes, Math. Comp. 68 (1999) 417-427.

Cf. A000045, A001605, A117595.

Cf. A001602, A022307, A030427, A051694, A075737, A083668, A099000.

[n: n in [0..1000] | IsPrime(Fibonacci(2*n+1))]; // Vincenzo Librandi, May 24 2016

Select[Range[0, 5000], PrimeQ[Fibonacci[2 # + 1]] &] (* Vincenzo Librandi, May 24 2016 *)

a(n) = (A083668(n)-1)/2. - R. J. Mathar, Jul 08 2009

a(n) = (A001605(n+1)-1)/2, n > 1. - Vincenzo Librandi, May 24 2016

More terms from Vincenzo Librandi, May 24 2016

cp's OEIS Frontend

A117517 Numbers k such that F(2*k + 1) is prime where F(m) is a Fibonacci number.

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