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A178576 Primes that are the sum of two Fibonacci numbers.

%I A178576 #27 May 13 2013 01:54:11
%S A178576 2,3,5,7,11,13,23,29,37,47,89,97,149,157,199,233,241,379,521,613,631,
%T A178576 1021,1597,1741,2207,3571,9349,10949,11933,17713,28657,46381,46457,
%U A178576 46601,50549,75169,196439,203183,214129,514229,560597,832129,2178343
%N A178576 Primes that are the sum of two Fibonacci numbers.
%C A178576 The corresponding prime indices are in A178971.
%H A178576 Charles R Greathouse IV, <a href="/A178576/b178576.txt">Table of n, a(n) for n = 1..5624</a>
%e A178576 Prime 613 can be expressed as 3+610 = Fibonacci(4)+Fibonacci(15), therefore 613 is in the sequence.
%t A178576 f=Fibonacci[Range[33]]; Select[Union[Flatten[Outer[Plus, f, f]]], PrimeQ]
%o A178576 (PARI) list(lim)={
%o A178576     my(v,u=List(),t);
%o A178576     v=vector(log(lim*sqrt(5))\log((1+sqrt(5))/2)+1,n,fibonacci(n));
%o A178576     for(i=1,#v,for(j=i+1,#v,
%o A178576         t = v[i] + v[j];
%o A178576         if(t > lim, break);
%o A178576         if(ispseudoprime(t),listput(u, t))
%o A178576     ));
%o A178576     vecsort(Vec(u),,8)
%o A178576 }; \\ _Charles R Greathouse IV_, Jul 23 2012
%Y A178576 Cf. A000040, A000045, A178971. Subsequence of A059389.
%K A178576 nonn
%O A178576 1,1
%A A178576 _Carmine Suriano_, Jan 12 2011