A243181 Numbers of the form 4x^2+9xy-11y^2.

0, 2, 4, 8, 11, 13, 16, 17, 18, 22, 23, 26, 29, 31, 32, 34, 36, 44, 46, 50, 52, 58, 59, 62, 64, 68, 72, 73, 79, 88, 89, 92, 98, 99, 100, 104, 116, 117, 118, 121, 122, 124, 128, 134, 136, 137, 139, 143, 144, 146, 153, 158, 162, 169, 173, 176, 178, 184, 187, 196, 198, 199, 200, 207, 208, 211, 221, 223, 226, 232, 234, 236, 239, 242, 244, 248, 253, 256, 261, 268

Offset: 1

Author

N. J. A. Sloane, Jun 02 2014

Keywords

• nonn

Comments

Discriminant 257.

16*a(n) has the form z^2 - 257*y^2, where z = 8*x+9*y. [Bruno Berselli, Jun 20 2014]

Links

• R. J. Mathar, Table of n, a(n) for n = 1..2180
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A141168.

Programs

Mathematica

maxTerm = 300; m0 = 10; dm = 10; Clear[f]; f[m_] := f[m] = Table[4*x^2 + 9 x*y - 11*y^2 , {x, -m, m}, {y, -m, m}] // Flatten // Union // Select[#, 0 <= # <= maxTerm&]&; f[m0]; f[m = m0]; While[f[m] != f[m - dm], m = m + dm]; f[m] (* Jean-François Alcover, Jun 04 2014 *) (* Brute force search, so not guaranteed to find all solutions, I believe. - N. J. A. Sloane, Jun 05 2014 *)
Reap[For[n = 0, n <= 30, n++,
   If[Reduce[4*x^2 + 9*x*y - 11*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]] (* Better program, not brute force, but slow. Confirms the terms up through 29. - N. J. A. Sloane, Jun 05 2014 *)