A263467 Indices of Fibonacci primes equal to a sum of squares of two Fibonacci numbers at least one of which is also prime.

5, 7, 11, 13, 23, 47

Offset

1,1

Comments

Same as odd numbers m such that at least two of the Fibonacci numbers F(m), F((m-1)/2), F((m+1)/2) are prime (because F(2k+1) = F(k)^2 + F(k+1)^2).

The terms are primes (because F(a*b)= F(a) * F(b)).

No other terms up to 2904353.

The corresponding Fibonacci primes are in A263468.

Links

Table of n, a(n) for n=1..6.

Wikipedia, Fibonacci number

Wikipedia, Fibonacci prime

Formula

A000045(a(n)) = A263468(n).

Example

F(7) = 13 = 2^2 + 3^2 = F(3)^2 + F(4)^2, so 7 is a member.
F(47) = 2971215073 = 28657^2 + 46368^2 = F(23)^2 + F(24)^2 and 2971215073 and 28657 are prime, so 47 is a member.

Crossrefs

Cf. A000045, A001605, A005478, A002144, A002313, A263468.

Sequence in context: A098865 A022885 A176831 * A200143 A265780 A135774

Adjacent sequences: A263464 A263465 A263466 * A263468 A263469 A263470

Keyword

nonn,more

Author

Jonathan Sondow, Nov 04 2015

Status

approved