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A263467 Indices of Fibonacci primes equal to a sum of squares of two Fibonacci numbers at least one of which is also prime. 1
5, 7, 11, 13, 23, 47 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 14 00:07 EDT 2021. Contains 342941 sequences. (Running on oeis4.)