A279795 Numbers n such that F(n) and F(n-2) are both prime where F(n) = A000045(n).

5, 7, 13, 433, 571

Offset

1,1

Comments

a(6) > 2904353. - Daniel Suteu, Dec 23 2016

Terms n of A001605 such that n-2 is also a term of A001605. Surprisingly, the first 4 terms minus 2, { 3, 5, 11, 431 }, are the first four terms of A101315 which also relates to simultaneously prime { m+2, F(m) and F(m)+2 }, but where F is a different function, m -> (m-1)^2 + 1. - M. F. Hasler, Dec 24 2016

Larger primes of the Fibonacci prime pairs in A073340. - Bobby Jacobs, Jan 18 2017

Links

Table of n, a(n) for n=1..5.

Formula

a(n) = A281087(n) + 2. - Bobby Jacobs, Jan 18 2017

Example

13 is a term because Fibonacci(13) = 233 and Fibonacci(11) = 89 are both prime.

Mathematica

Select[Range[10^4], Times @@ Boole@ Map[PrimeQ@ Fibonacci@ # &, {#, # - 2}] > 0 &] (* Michael De Vlieger, Jan 21 2017 *)
Flatten[Position[Partition[Fibonacci[Range[580]], 3, 1], _?(AllTrue[ {#[[1]], #[[3]]}, PrimeQ]&), 1, Heads->False]]+2 (* Harvey P. Dale, Oct 01 2021 *)

Prog

(PARI) isok(n) = isprime(fibonacci(n)) && isprime(fibonacci(n-2)); \\ Michel Marcus, Jan 14 2017

Crossrefs

Cf. A000045, A001605, A006512, A073340, A101315, A281087.

Sequence in context: A342506 A158892 A106022 * A050085 A314331 A314332

Adjacent sequences: A279792 A279793 A279794 * A279796 A279797 A279798

Keyword

more,nonn

Author

Altug Alkan, Dec 18 2016

Status

approved