A119984 Numbers k such that Fibonacci(prime(k)) is prime.

2, 3, 4, 5, 6, 7, 9, 10, 14, 15, 23, 32, 33, 72, 83, 84, 87, 97, 104, 105, 429, 637, 710, 1152, 1194, 1692, 2814, 3316, 3824, 3971, 5206, 8002, 10016, 12161, 13681, 18069, 33653, 36467, 48355, 48629, 49455, 73574, 82128, 99005, 123685, 135276, 146779, 210404, 233207, 239581

Offset: 1

Author

Alexander Adamchuk, Aug 04 2006

Keywords

• nonn

Comments

All prime Fibonacci numbers have prime indices, except prime F(4) = 3; a(n) is such that Fibonacci(prime(a(n))) is prime. - Robert G. Wilson v, Aug 05 2006

Links

• Amiram Eldar, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A000045, A000720, A001605, A005478, A030426, A075737, A083668.

Programs

Mathematica

Select[ Range@3000, PrimeQ@ Fibonacci@ Prime@ # &] (* Robert G. Wilson v, Aug 05 2006 *)

Formula

a(n) = pi(A001605(n+1)). This holds for all n including n=1, since pi(4) = pi(3) = 2. - Jens Kruse Andersen, Jul 24 2014

Extensions

a(21)-a(27) from Robert G. Wilson v, Aug 05 2006

More terms (from A001605) from T. D. Noe, Aug 18 2006

a(42)-a(48) (from A001605, found by Henri Lifchitz) from Jens Kruse Andersen, Jul 24 2014

a(49)-a(50) (from A001605, found by Henri Lifchitz) from Amiram Eldar, Sep 01 2019