A028958 Numbers represented by quadratic form with Gram matrix [ 2, 1; 1, 12 ] (divided by 2).

0, 1, 4, 6, 8, 9, 12, 16, 18, 23, 24, 25, 26, 27, 32, 36, 39, 48, 49, 52, 54, 58, 59, 62, 64, 72, 78, 81, 82, 87, 92, 93, 94, 96, 100, 101, 104, 108, 116, 117, 121, 123, 124, 128, 138, 141, 142, 144, 146, 150, 156, 162, 164, 167, 169, 173, 174, 184, 186, 188, 192

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Nonnegative integers of the form x^2 + x*y + 6*y^2, discriminant -23. - Ray Chandler, Jul 12 2014

The Gram matrix is positive-definite, therefore, if w := (1 + sqrt(-23)) / 2, then |x + w*y|^2 = x^2 + x*y + 6*y^2 > 0 for all integers x and y except x = y = 0. - Michael Somos, Mar 28 2015

The theta function of the lattice with basis [1, w] is the g.f. of A028959, therefore, A028959(n) is positive if and only if n is in this sequence. - Michael Somos, Mar 28 2015

Links

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

Crossrefs

For primes see A033217. Cf. A028929, A106867.

Cf. A028959.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000