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

Author

Hugo Pfoertner, Jul 14 2019

Keywords

• nonn

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)

Crossrefs

Primes in this sequence: A141166.

Programs

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 *)