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%I #31 Aug 28 2012 19:53:14
%S 1,3,5,9,13,17,27,29,37,41,53,61,65,89,97,113,123,137,157,169,185,197,
%T 267,281,289,305,313,349,353,369,397,411,433,457,461,481,493,509,541,
%U 557,593,613,617,661,673,697,809,829,841,857,877,901,1061,1097
%N Odd numbers n such that the Lucas number L(n) can be written in the form a^2 + 2*b^2.
%C These Lucas numbers L(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[1, 200, 2], Length[FindInstance[x^2 + 2*y^2 == LucasL[#], {x, y}, Integers]] > 0 &] (* _T. D. Noe_, Aug 27 2012 *)
%o (PARI) for(i=2, 500, a=factorint(fibonacci(i-1)+fibonacci(i+1))~; has=0; for(j=1, #a, if(a[1, j]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==1, print(i", ")))
%Y Cf. A000032, A215813.
%K nonn
%O 1,2
%A _V. Raman_, Aug 23 2012
%E 1 added by _T. D. Noe_, Aug 27 2012
%E Added 27 more terms - _V. Raman_, Aug 28 2012
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