A244780 Positive numbers primitively represented by the binary quadratic form (1, 1, 3).

1, 3, 5, 9, 11, 15, 23, 25, 27, 31, 33, 37, 45, 47, 53, 55, 59, 67, 69, 71, 75, 81, 89, 93, 97, 99, 103, 111, 113, 115, 125, 135, 137, 141, 155, 157, 159, 163, 165, 177, 179, 181, 185, 191, 199, 201, 207, 213, 223, 225, 229, 235, 243, 251, 253, 257, 265, 267

Offset: 1

Author

Peter Luschny, Jul 06 2014

Keywords

• nonn

Comments

Discriminant = -11.

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A244779, A244819.

Programs

Maple

# Function PriRepBQF in A244779.
A244780_list := n -> PriRepBQF(1, 1, 3, n); A244780_list(267);

Mathematica

Reap[For[n = 1, n < 1000, n++, r = Reduce[x^2 + x y + 3 y^2 == n, {x, y}, Integers]; If[r =!= False, If[AnyTrue[{x, y} /. {ToRules[r /. C[1] -> 0]}, CoprimeQ @@ # &], Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)