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%I #14 Apr 19 2020 16:31:41
%S 2,4,11,17,19,41,113,313,353,617,1097,1361,4787,4793,5851,8467,10691,
%T 12251,13963,14449,35449,36779,44507,51169,56003,89849,140057,148091,
%U 159521,183089,193201,202667,387433,443609,574219,616787,692147
%N Numbers n such that the n-th Lucas number is prime and can be written in the form a^2 + 3*b^2.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci">Factorizations of Fibonacci and Lucas numbers</a>
%t Select[Range[693000],PrimeQ[LucasL[#]]&&Length[Solve[{a^2+3b^2==LucasL[#],a>=0,b>=0},{a,b},Integers]]>0&] (* _Harvey P. Dale_, Apr 19 2020 *)
%Y Cf. A000032, A001606.
%K nonn
%O 1,1
%A _V. Raman_, Sep 08 2012