A243705 Nonnegative numbers represented by the indefinite quadratic form 3x^2+13xy-3y^2.

0, 3, 7, 12, 13, 15, 17, 27, 28, 35, 47, 48, 52, 53, 60, 63, 65, 67, 68, 75, 85, 93, 97, 108, 112, 117, 123, 135, 137, 140, 147, 153, 157, 167, 175, 177, 183, 188, 192, 193, 208, 212, 217, 227, 233, 235, 240, 243, 252, 257, 260, 263, 265, 268

Offset: 1

Author

N. J. A. Sloane, Jun 17 2014

Keywords

• nonn

Comments

Discriminant 205.

12*a(n) has the form z^2 - 205*y^2, where z = 6*x+13*y. In fact, this is a particular case of the following identity on the numbers of the form a*x^2+b*x*y+c*y^2: 4*a*(a*x^2+b*x*y+c*y^2) = (2*a*x+b*y)^2-(b^2 -4*a*c)*y^2. [Bruno Berselli, Jun 20 2014]

Links

• Will Jagy, C++ program Conway_Positive_All.cc to find all positive numbers represented by an indefinite binary quadratic form
• Will Jagy, Sample output from Conway_Positive_All.cc
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A243706.