A243180 Numbers of the form 8x^2+xy-8y^2.

0, 1, 4, 8, 9, 16, 22, 25, 26, 32, 34, 36, 44, 46, 49, 52, 58, 61, 62, 64, 67, 68, 72, 81, 88, 92, 100, 104, 113, 116, 118, 121, 124, 128, 136, 143, 144, 146, 157, 158, 169, 176, 178, 184, 187, 193, 196, 197, 198, 200, 208, 221, 225, 227, 232, 234, 236, 241, 242, 244, 248, 253, 256, 257, 268, 272, 274, 278, 286, 288, 289, 292, 299, 306, 316, 319, 324, 338, 341

Offset: 1

Author

N. J. A. Sloane, Jun 02 2014

Keywords

• nonn

Comments

Discriminant 257.

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

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1676
• Peter Luschny, Binary Quadratic Forms
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A141167. Cf. A243181, A141168.

Programs

Mathematica

maxTerm = 400; m0 = 10; dm = 10; Clear[f]; f[m_] := f[m] = Table[8*x^2 + x*y - 8*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 *)

Sage

# uses[binaryQF]
# The function binaryQF is defined in the link 'Binary Quadratic Forms'.
Q = binaryQF([8, 1, -8])
print([0]+Q.represented_positives(341)) # Peter Luschny, Oct 26 2016