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

3, 5, 11, 431, 569

Offset: 1

Author

Bobby Jacobs, Jan 14 2017

Keywords

• more
• nonn

Comments

Smaller primes of the Fibonacci prime pairs in A073340.

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

Examples

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

Links

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

Crossrefs

First differs from A101315 at a(5).

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

Programs

Mathematica

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 *)

Formula

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

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