A263468 Fibonacci primes equal to a sum of squares of two Fibonacci numbers at least one of which is also prime.

5, 13, 89, 233, 28657, 2971215073

Offset

1,1

Comments

Same as Fibonacci numbers F(2k+1) such that at least two of the numbers F(2k+1), F(k), F(k+1) are prime (because F(2k+1) = F(k)^2 + F(k+1)^2 and F(a*b)= F(a) * F(b))). Thus the two squares are of consecutive Fibonacci numbers.

No other terms up to F(2904353).

The corresponding Fibonacci indices are in A263467.

Subsequence of A002144 and A002313.

Links

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

Wikipedia, Fibonacci number

Wikipedia, Fibonacci prime

Formula

a(n) = A000045(A263467(n)).

Example

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

Crossrefs

Cf. A000045, A001605, A002144, A002313, A005478, A263467.

Sequence in context: A165262 A092955 A190949 * A350467 A081560 A057624

Adjacent sequences: A263465 A263466 A263467 * A263469 A263470 A263471

Keyword

nonn,more

Author

Jonathan Sondow, Nov 04 2015

Status

approved