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

%I #35 Dec 16 2024 14:26:51

%S 0,2,5,7,8,13,18,20,28,32,37,45,47,50,52,58,63,67,70,72,73,80,83,97,

%T 98,112,117,122,125,128,130,137,145,148,158,162,163,167,175,180,182,

%U 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

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

%C Discriminant 65.

%H Vincenzo Librandi, <a href="/A243171/b243171.txt">Table of n, a(n) for n = 1..1500</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t 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 *)

%t 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 *)

%Y Primes in this sequence = A141112.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 01 2014

%E Missing a(63)=307 inserted by _Vincenzo Librandi_, Dec 08 2024