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
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
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Apr 26 2006
EXTENSIONS
More terms from Vincenzo Librandi, May 24 2016
STATUS
approved