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

1,2

Comments

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

Links

Table of n, a(n) for n=1..56.

Example

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.

Prog

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

Crossrefs

Cf. A000040, A003136, A267137.

Sequence in context: A215631 A081695 A290955 * A142958 A310214 A310215

Adjacent sequences: A270119 A270120 A270121 * A270123 A270124 A270125

Keyword

nonn

Author

Altug Alkan, Mar 11 2016

Status

approved