A216552 Numbers n such that the n-th Fibonacci number is prime and can be written in the form a^2 + 3*b^2.

4, 7, 17, 23, 47, 137, 359, 431, 433, 449, 569, 9311, 14431, 25561, 35999, 37511, 50833, 81839, 104911, 590041, 593689, 604711, 1049897, 1285607, 1636007, 1968721

Offset

1,1

Comments

Primes are of the form a^2 + 3*b^2 if and only if they are not of the form 3k + 2 (cf. A003136), and Fibonacci(n) = 2 (mod 3) if and only if n is in A047443 (i.e., n = 3, 5 or 6 (mod 8)), so the second condition can be considerably simplified. - M. F. Hasler, Sep 29 2012

Links

Table of n, a(n) for n=1..26.

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Formula

A216552 = A001605 \ A047443 = { n in A001605 | A000045(n) != 2 (mod 3) } = { n in A001605 | A000045(n) is in A003136 } . - M. F. Hasler, Sep 29 2012

Prog

(PARI) is_A216552(n) = !bittest(104, n%8) & is_A001605(n) \\ - M. F. Hasler, Sep 29 2012

Crossrefs

Cf. A000045, A001605, A003136.

Sequence in context: A363642 A124402 A349610 * A034736 A236564 A302549

Adjacent sequences: A216549 A216550 A216551 * A216553 A216554 A216555

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved