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

3, 11, 31, 41, 103, 131, 167, 223, 503, 521, 563, 601, 677, 739, 829, 911, 1361, 1439, 1511, 1613, 1741, 1913, 1931, 2441, 2939, 3191, 3391, 3413, 3499, 3671, 3823, 4007, 4229, 4871, 4931, 4969, 5231, 5851, 6047, 6301, 6329, 7079, 7331, 7523, 7759, 8087, 8263, 8543, 9281, 9283

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

11 is a term because 2^3 + 2*1 + 1^3 = 11 is prime.
31 is a term because 3^3 + 3*1 + 1^3 = 31 is prime.
41 is a term because 3^3 + 3*2 + 2^3 = 41 is prime.

Mathematica

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 *)
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 *)

Crossrefs

Cf. A007645, A300381.

Sequence in context: A003523 A018781 A119215 * A057172 A277167 A277049

Adjacent sequences: A266967 A266968 A266969 * A266971 A266972 A266973

Keyword

nonn

Author

Altug Alkan, Jan 07 2016

Status

approved