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

1,2

Comments

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

Links

Table of n, a(n) for n=1..48.

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A001605, A117595.

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

Sequence in context: A081830 A238006 A329289 * A339732 A098491 A280449

Adjacent sequences: A117514 A117515 A117516 * A117518 A117519 A117520

Keyword

nonn

Author

Parthasarathy Nambi, Apr 26 2006

Extensions

More terms from Vincenzo Librandi, May 24 2016

Status

approved