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%I #25 Aug 28 2012 19:47:24
%S 1,2,3,4,6,9,11,12,13,18,23,25,26,33,36,39,47,52,59,61,71,83,107,109,
%T 121,122,131,141,157,167,179,183,191,193,227,244,249,251,299,314,321,
%U 337,359,363,383,393,397,423,431,433,471,501,517,579,587,601,628,647,649,794,866,877,911,913,947,1079,1091,1093
%N Numbers n such that the Fibonacci number F(n) can be written in the form a^2 + 2*b^2.
%C These Fibonacci numbers F(n) have no prime factor congruent to 5 or 7 mod 8 to an odd power.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Fibonacci and Lucas factorizations</a>
%t Select[Range[200], Length[FindInstance[x^2 + 2 y^2 == Fibonacci[#], {x, y}, Integers]] > 0 &] (* _T. D. Noe_, Aug 27 2012 *)
%o (PARI) for(i=2, 500, a=factorint(fibonacci(i))~; has=0; for(j=1, #a, if(a[1, j]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))
%Y Cf. A000045, A215819, A215820, A215821.
%K nonn
%O 1,2
%A _V. Raman_, Aug 23 2012
%E 1 added by _T. D. Noe_, Aug 27 2012
%E Added the number 25 and 24 more terms - V. Raman, Aug 28 2012
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