A309136 Nonnegative integers of the form x^2+15*x*y-y^2.

0, 1, 4, 9, 15, 16, 25, 27, 33, 36, 37, 45, 49, 51, 53, 55, 57, 60, 64, 75, 81, 85, 95, 99, 100, 108, 121, 125, 129, 132, 135, 144, 148, 153, 165, 169, 171, 173, 180, 183, 187, 193, 196, 204, 209, 212, 213, 215, 220, 225, 228, 229, 240, 241, 243, 249, 255, 256

Offset

1,3

Comments

Discriminant of indefinite binary quadratic form: 229.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1268

Will Jagy, C++ program Conway_Positive_All.cc to find all positive numbers represented by an indefinite binary quadratic form

Peter Luschny, Binary Quadratic Forms

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

Mathematica

Reap[For[n=0, n<=58, n++, If[Reduce[x^2+15*x*y-y^2==n, {x, y}, Integers]=!=False, Sow[n]]]][[2, 1]] (* Vincenzo Librandi, Nov 16 2024 *)
sol[t_]:=Solve[x^2+15*x*y-y^2==t, {x, y}, Integers]; Select[Range[0, 256], sol[#]!={}&] (* Vincenzo Librandi, Nov 25 2024 *)

Prog

(C++) See Jagy link.

Crossrefs

Primes in this sequence: A141166.

Sequence in context: A243173 A345452 A313156 * A313157 A313158 A313159

Adjacent sequences: A309133 A309134 A309135 * A309137 A309138 A309139

Keyword

nonn

Author

Hugo Pfoertner, Jul 14 2019

Status

approved