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%I #22 May 02 2013 13:08:48
%S 4,7,17,23,47,137,359,431,433,449,569,9311,14431,25561,35999,37511,
%T 50833,81839,104911,590041,593689,604711,1049897,1285607,1636007,
%U 1968721
%N Numbers n such that the n-th Fibonacci number is prime and can be written in the form a^2 + 3*b^2.
%C 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
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Factorizations of Fibonacci and Lucas numbers</a>
%F 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
%o (PARI) is_A216552(n) = !bittest(104,n%8) & is_A001605(n) \\ - _M. F. Hasler_, Sep 29 2012
%Y Cf. A000045, A001605, A003136.
%K nonn
%O 1,1
%A _V. Raman_, Sep 08 2012
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