A101315 -id:A101315 - cp's OEIS frontend

A281087 Numbers k such that Fibonacci(k) and Fibonacci(k+2) are both prime.

3, 5, 11, 431, 569

Offset: 1

Bobby Jacobs, Jan 14 2017

Smaller primes of the Fibonacci prime pairs in A073340.

See the comment to A073340 - Harvey P. Dale, Jan 30 2025

			11 is in the sequence because Fibonacci(11) = 89 and Fibonacci(13) = 233 are both prime.

J. B. Cosgrave and K. Dilcher, Pairs of reciprocal quadratic congruences involving primes, Fig. Quart. 51 (2) (2013) 98-111

First differs from A101315 at a(5).

Cf. A000045, A001359, A001605, A073340, A101315, A279795.

Select[Range[600],PrimeQ[Fibonacci[#]] && PrimeQ[Fibonacci[#+2]] &] (* Stefano Spezia, Nov 15 2024 *)
SequencePosition[Table[If[PrimeQ[Fibonacci[n]],1,0],{n,600}],{1,,1}][[;;,1]] (* _Harvey P. Dale, Jan 30 2025 *)

a(n) = A279795(n) - 2.

a(n) = A073340(2n-1).

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

Original entry on oeis.org

5, 7, 13, 433, 571

Offset: 1

Altug Alkan, Dec 18 2016

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

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

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

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 *)

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

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

cp's OEIS Frontend

A281087 Numbers k such that Fibonacci(k) and Fibonacci(k+2) are both prime.

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