%I #29 Aug 28 2012 19:54:03
%S 2,3,11,17,19,41,43,67,73,83,113,139,241,281,283,313,353,379,401,443,
%T 457,569,571,577,617,857,881,1009,1033,1097
%N Prime numbers n such that the Lucas number L(n) can be written in the form a^2 + 3*b^2.
%C These Lucas numbers L(n) have no prime factor congruent to 2 mod 3 to an odd power.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Fibonacci and Lucas factorizations</a>
%o (PARI) forprime(i=2, 500, a=factorint(fibonacci(i-1)+fibonacci(i+1))~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i", ")))
%Y Cf. A000032, A215810, A215815, A215816.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 3 added by _T. D. Noe_, Aug 27 2012
%E Added 12 more terms - _V. Raman_, Aug 28 2012
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