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

1, 3, 7, 12, 13, 24, 25, 26, 33, 35, 45, 50, 51, 53, 55, 59, 60, 77, 79, 80, 82, 84, 87, 88, 104, 106, 113, 116, 121, 123, 127, 135, 136, 140, 148, 152, 159, 165, 169, 174, 176, 178, 184, 186, 189, 204, 209, 211, 212, 216, 218, 221, 223, 226, 227, 237

Offset: 1

Author

Altug Alkan, Mar 11 2016

Keywords

• nonn

Comments

How is the distribution of a(n), a(n+1) in this sequence where a(n+1) = a(n) + 1?

Examples

			1 is a term because prime(1) = 2 = (-2)^2 + (-2) + (-2)*1 + 1 + 1^2.
3 is a term because prime(3) = 5 = 1^2 + 1 + 1*1 + 1 + 1^2.
7 is a term because prime(7) = 17 = (-5)^2 + (-5) + (-5)*3 + 3 + 3^2.
12 is a term because prime(12) = 37 = (-7)^2 + (-7) + (-7)*5 + 5 + 5^2.
13 is a term because prime(13) = 41 = 7^2 + 7 + 7*(-3) + (-3) + (-3)^2.
		

Crossrefs

Cf. A000040, A003136, A267137.

Programs

PARI

isA003136(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
for(n=1, 250, if(isA003136(3*prime(n)+1), print1(n, ", ")));