A244146 Primes of the form x^2 + x*y + y^2 with x, y primes.

19, 67, 79, 109, 163, 199, 349, 433, 457, 607, 691, 739, 937, 997, 1063, 1093, 1327, 1423, 1447, 1489, 1579, 1753, 1777, 1987, 2017, 2089, 2203, 2287, 2383, 2749, 3229, 3463, 3847, 3943, 4051, 4177, 4513, 4567, 5347, 5413, 5479, 5557, 5653, 6079, 6133, 6271, 6661

Offset

1,1

Comments

Equally: primes that are of the form (p+q)^2 - p*q, with p, q primes. - Antti Karttunen, Jun 21 2014

Links

Jean-François Alcover, Table of n, a(n) for n = 1..2089

Example

The terms 19, 67, 79 and 1777753 are in the sequence because they can be represented as:
19 = 2^2 + 2*3 + 3^2 = (2+3)^2 - 2*3.
67 = 2^2 + 2*7 + 7^2 = (2+7)^2 - 2*7.
79 = 3^2 + 3*7 + 7^2 = (3+7)^2 - 3*7.
1777753 = 677^2 + 677*859 + 859^2 = (677+859)^2 - 677*859.

Mathematica

Reap[For[p = 2, p < 10^4, p = NextPrime[p], If[Reduce[p == x^2 + x y + y^2, {x, y}, Primes] =!= False, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jul 12 2019 *)

Crossrefs

Subsequence of A007645.

Cf. A045331.

Sequence in context: A093485 A226633 A156967 * A104047 A239714 A201781

Adjacent sequences: A244143 A244144 A244145 * A244147 A244148 A244149

Keyword

nonn

Author

Peter Luschny, Jun 21 2014

Status

approved