%I #32 Jan 04 2022 21:57:33
%S 2,3,5,13,17,29,37,41,53,61,89,97,113,137,157,197,281,313,349,353,397,
%T 433,457,461,509,541,557,593,613,617,661,673,809,829,857,877,1061,1097
%N Prime numbers p such that the Lucas number L(p) can be written in the form a^2 + 2*b^2.
%C These Lucas numbers L(p) 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>
%o (PARI) forprime(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, A215812.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 18 more terms from _V. Raman_, Aug 28 2012