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A266970 Primes of the form x^3 + x*y + y^3 where x and y are positive integers.

%I A266970 #14 Mar 07 2018 04:09:08
%S A266970 3,11,31,41,103,131,167,223,503,521,563,601,677,739,829,911,1361,1439,
%T A266970 1511,1613,1741,1913,1931,2441,2939,3191,3391,3413,3499,3671,3823,
%U A266970 4007,4229,4871,4931,4969,5231,5851,6047,6301,6329,7079,7331,7523,7759,8087,8263,8543,9281,9283
%N A266970 Primes of the form x^3 + x*y + y^3 where x and y are positive integers.
%e A266970 11 is a term because 2^3 + 2*1 + 1^3 = 11 is prime.
%e A266970 31 is a term because 3^3 + 3*1 + 1^3 = 31 is prime.
%e A266970 41 is a term because 3^3 + 3*2 + 2^3 = 41 is prime.
%t A266970 nn = 10000; lim = Floor[nn^(1/3)]; Union[Reap[Do[p = a^3 + a*b + b^3; If[p <= nn && PrimeQ[p], Sow[p]], {a, lim}, {b, a}]][[2, 1]]] (* _Wesley Ivan Hurt_, Jan 07 2016 after _T. D. Noe_ *)
%t A266970 lim=100; Select[Union[Flatten[Table[x^3 + x y + y^3, {x, 0, lim}, {y, 0, lim}]]], #>0 && #<lim^2 && PrimeQ[#] &] (* _Vincenzo Librandi_, Jan 08 2016 *)
%Y A266970 Cf. A007645, A300381.
%K A266970 nonn
%O A266970 1,1
%A A266970 _Altug Alkan_, Jan 07 2016