A201719 - OEIS

%I #12 Oct 30 2018 10:31:02

%S 11,19,43,59,67,83,107,139,163,179,211,251,307,331,419,443,467,491,

%T 563,571,587,619,643,811,883,907,947,971,1019,1091,1123,1171,1259,

%U 1291,1307,1427,1531,1571,1579,1667,1699,1747,1787,1811,1907,1979,1987,2003,2011

%N Primes of the form x^2 + 2y^2 such that y^2 + 2x^2 is also prime.

%C All terms == 3 mod 8 (cf. A007520).

%H Zak Seidov, <a href="/A201719/b201719.txt">Table of n, a(n) for n = 1..10000</a>

%e Corresponding pairs of primes:

%e (a(1),a(2))=(11,19): 11=3^2+2*1^2, 19=1^2+2*3^2

%e (a(3),a(4))=(43,59): 43=5^2+2*3^2, 59=3^2+2*5^2

%e (a(5),a(7))=(67,107): 67=7^2+2*3^2, 107=3^2+2*7^2.

%t With[{nn=50},Take[Union[Flatten[Select[{#[[1]]^2+2#[[2]]^2,2#[[1]]^2+ #[[2]]^2}&/@Subsets[Range[nn],{2}],And@@PrimeQ[#]&]]],nn]] (* _Harvey P. Dale_, Sep 15 2013 *)

%Y Cf. A154777.

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 04 2011