A243701 -id:A243701 - cp's OEIS frontend

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

N. J. A. Sloane, Jun 17 2014

nonn

Discriminant 205.

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)

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

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

A372518 Positive numbers primitively represented by the indefinite quadratic form x^2 + 13xy - 9y^2.

Original entry on oeis.org

1, 5, 21, 39, 51, 59, 81, 91, 105, 119, 131, 139, 141, 159, 189, 195, 201, 221, 241, 255, 269, 271, 279, 291, 295, 329, 351, 359, 369, 371, 405, 409, 411, 441, 455, 459, 469, 471, 501, 541, 549, 569, 579, 595, 599, 611, 651, 655, 661, 679, 681, 689, 695, 699

Offset: 1

Peter Luschny, May 04 2024

nonn

Discriminant 205.

Peter Luschny, Binary Quadratic Forms, GitHub 2024.

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

load('https://raw.githubusercontent.com/PeterLuschny/BinaryQuadraticForms/main/BinaryQF.sage')
Q = binaryQF([1, 13, -9])
print(Q.represented_positives(700, 'primitively'))

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

SageMath