A094810 Primes of the form F(k)*F(k+1) + F(k+2) where F(x) = Fibonacci(x).

3, 5, 11, 23, 53, 307, 769, 5039, 13049, 603667, 1578823, 10810469, 427860443429, 16944504081930151, 31525215457325198354227, 33014537901332492765899179111315710183929325703531042557, 929153004165028209140476861623544319436354594054815247101152031731

Offset

1,1

Comments

Excluding the term a(4)=23, primes p such that p(n) is not a sum of two squares but p(n+1) is a sum of two squares.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..23

Formula

A000040 INTERSECT A305412. - R. J. Mathar, Nov 14 2019

Example

5 is in the sequence because F(2)*F(3)+F(4) = 1*2+3=5.
11 is in because F(3)*F(4)+F(5) = 2*3+5 = 11.
23 is in because F(4)*F(5)+F(6) = 3*5+8 = 23.

Mathematica

Select[#[[1]]#[[2]]+#[[3]]&/@Partition[Fibonacci[Range[60]], 3, 1], PrimeQ] (* Harvey P. Dale, Mar 03 2026 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (isprime(p=fibonacci(n)*fibonacci(n+1) +fibonacci(n+2)), print1(p, ", ")); ); } \\ Michel Marcus, Jun 03 2013

Crossrefs

Cf. A000040, A305412.

Sequence in context: A113151 A269964 A305412 * A139376 A074892 A074874

Adjacent sequences: A094807 A094808 A094809 * A094811 A094812 A094813

Keyword

nonn

Author

Giovanni Teofilatto, Jun 11 2004

Extensions

More terms from Michel Marcus, Jun 03 2013

Definition clarified by Harvey P. Dale, Mar 03 2026

Status

approved