A243702 Nonnegative numbers represented by the indefinite quadratic form x^2 + 13xy - 9y^2.

0, 1, 4, 5, 9, 16, 20, 21, 25, 36, 39, 45, 49, 51, 59, 64, 80, 81, 84, 91, 100, 105, 119, 121, 125, 131, 139, 141, 144, 156, 159, 169, 180, 189, 195, 196, 201, 204, 221, 225, 236, 241, 245, 255, 256, 269, 271, 279, 289, 291, 295, 320, 324, 329, 336, 351, 359

Offset

1,3

Comments

Discriminant 205.

Links

Table of n, a(n) for n=1..57.

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

Peter Luschny, Binary Quadratic Forms, GitHub 2024.

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

Prog

(C++) // Jagy's program, see link.
// Conway_Positive_All 1 13 -9 500
(SageMath)
load('https://raw.githubusercontent.com/PeterLuschny/BinaryQuadraticForms/main/BinaryQF.sage')
Q = binaryQF([1, 13, -9])
print(Q.represented_positives(360, 'all'))  # '0' is missing as indicated by the function name. #  Peter Luschny, May 04 2024

Crossrefs

Cf. A243701 (primes), A243702 (this sequence), A372518 (primitively).

Sequence in context: A087948 A010437 A020682 * A155565 A278336 A051216

Adjacent sequences: A243699 A243700 A243701 * A243703 A243704 A243705

Keyword

nonn,changed

Author

N. J. A. Sloane, Jun 17 2014

Status

approved