A117517 - OEIS

%I #24 Sep 08 2022 08:45:24

%S 1,2,3,5,6,8,11,14,21,23,41,65,68,179,215,216,224,254,284,285,1485,

%T 2361,2693,4655,4838,7215,12780,15378,17999,18755,25416,40919,52455,

%U 65010,74045,100553,198689,216890,295020,296844,302355,465758,524948,642803,818003,901529,984360,1452176

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

%C 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

%H H. Dubner and W. Keller, <a href="http://dx.doi.org/10.1090/S0025-5718-99-00981-3">New Fibonacci and Lucas Primes</a>, Math. Comp. 68 (1999) 417-427.

%F a(n) = (A083668(n)-1)/2. - _R. J. Mathar_, Jul 08 2009

%F a(n) = (A001605(n+1)-1)/2, n > 1. - _Vincenzo Librandi_, May 24 2016

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

%t Select[Range[0, 5000], PrimeQ[Fibonacci[2 # + 1]] &] (* _Vincenzo Librandi_, May 24 2016 *)

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

%Y Cf. A000045, A001605, A117595.

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

%K nonn

%O 1,2

%A _Parthasarathy Nambi_, Apr 26 2006

%E More terms from _Vincenzo Librandi_, May 24 2016