cp's OEIS Frontend

A270122 Indices of prime numbers of the form x^2 + x + x*y + y + y^2 where x and y are integers.

%I A270122 #9 Mar 16 2016 16:55:58
%S A270122 1,3,7,12,13,24,25,26,33,35,45,50,51,53,55,59,60,77,79,80,82,84,87,88,
%T A270122 104,106,113,116,121,123,127,135,136,140,148,152,159,165,169,174,176,
%U A270122 178,184,186,189,204,209,211,212,216,218,221,223,226,227,237
%N A270122 Indices of prime numbers of the form x^2 + x + x*y + y + y^2 where x and y are integers.
%C A270122 How is the distribution of a(n), a(n+1) in this sequence where a(n+1) = a(n) + 1?
%e A270122 1 is a term because prime(1) = 2 = (-2)^2 + (-2) + (-2)*1 + 1 + 1^2.
%e A270122 3 is a term because prime(3) = 5 = 1^2 + 1 + 1*1 + 1 + 1^2.
%e A270122 7 is a term because prime(7) = 17 = (-5)^2 + (-5) + (-5)*3 + 3 + 3^2.
%e A270122 12 is a term because prime(12) = 37 = (-7)^2 + (-7) + (-7)*5 + 5 + 5^2.
%e A270122 13 is a term because prime(13) = 41 = 7^2 + 7 + 7*(-3) + (-3) + (-3)^2.
%o A270122 (PARI) isA003136(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
%o A270122 for(n=1, 250, if(isA003136(3*prime(n)+1), print1(n, ", ")));
%Y A270122 Cf. A000040, A003136, A267137.
%K A270122 nonn
%O A270122 1,2
%A A270122 _Altug Alkan_, Mar 11 2016