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%I #15 Jul 12 2019 07:18:08
%S 19,67,79,109,163,199,349,433,457,607,691,739,937,997,1063,1093,1327,
%T 1423,1447,1489,1579,1753,1777,1987,2017,2089,2203,2287,2383,2749,
%U 3229,3463,3847,3943,4051,4177,4513,4567,5347,5413,5479,5557,5653,6079,6133,6271,6661
%N Primes of the form x^2 + x*y + y^2 with x, y primes.
%C Equally: primes that are of the form (p+q)^2 - p*q, with p, q primes. - _Antti Karttunen_, Jun 21 2014
%H Jean-François Alcover, <a href="/A244146/b244146.txt">Table of n, a(n) for n = 1..2089</a>
%e The terms 19, 67, 79 and 1777753 are in the sequence because they can be represented as:
%e 19 = 2^2 + 2*3 + 3^2 = (2+3)^2 - 2*3.
%e 67 = 2^2 + 2*7 + 7^2 = (2+7)^2 - 2*7.
%e 79 = 3^2 + 3*7 + 7^2 = (3+7)^2 - 3*7.
%e 1777753 = 677^2 + 677*859 + 859^2 = (677+859)^2 - 677*859.
%t 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 *)
%Y Subsequence of A007645.
%Y Cf. A045331.
%K nonn
%O 1,1
%A _Peter Luschny_, Jun 21 2014
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