A243171 Nonnegative integers of the form 2*x^2+5*x*y-5*y^2.

0, 2, 5, 7, 8, 13, 18, 20, 28, 32, 37, 45, 47, 50, 52, 58, 63, 67, 70, 72, 73, 80, 83, 97, 98, 112, 117, 122, 125, 128, 130, 137, 145, 148, 158, 162, 163, 167, 175, 180, 182, 188, 193, 197, 200, 202, 203, 208, 223, 227, 232, 242, 245, 252, 262, 268, 278, 280, 288, 292, 293, 305, 307, 317, 320, 325, 332, 333, 338, 343, 353, 358, 362, 370, 377, 382, 383

Offset

1,2

Comments

Discriminant 65.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1500

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

Mathematica

Module[{k, r}, Reap[For[k=1, k<=100, k++, r=Reduce[k==2*x^2+5*x y-5* y^2, {x, y}, Integers]; If[r=!=False, (*Print[k, " ", r]; *)Sow[k]]]][[2, 1]]] (* Vincenzo Librandi, Nov 16 2024 *)
sol[t_]:=Solve[2*x^2+5*x*y-5*y^2==t, {x, y}, Integers]; Select[Range[0, 385], sol[#]!={}&] (* Vincenzo Librandi, Nov 25 2024 *)

Crossrefs

Primes in this sequence = A141112.

Sequence in context: A190900 A216572 A020674 * A005624 A275410 A139481

Adjacent sequences: A243168 A243169 A243170 * A243172 A243173 A243174

Keyword

nonn,changed

Author

N. J. A. Sloane, Jun 01 2014

Extensions

Missing a(63)=307 inserted by Vincenzo Librandi, Dec 08 2024

Status

approved