A243194 Nonnegative integers of the form x^2+xy+10y^2.

0, 1, 4, 9, 10, 12, 16, 22, 25, 30, 36, 39, 40, 43, 48, 49, 52, 55, 64, 66, 75, 81, 82, 88, 90, 94, 100, 103, 108, 118, 120, 121, 130, 139, 142, 144, 156, 157, 160, 165, 166, 169, 172, 178, 181, 183, 192, 196, 198, 205, 208, 220, 225, 235, 237, 244, 246, 250, 256, 264, 270, 274, 277, 282, 286, 289

Offset: 0

Author

N. J. A. Sloane, Jun 08 2014

Keywords

• nonn

Comments

Discriminant -39.

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..1611
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes: A033227.

Programs

Maple

fd:=proc(a,b,c,M) local dd,xlim,ylim,x,y,t1,t2,t3,t4,i;
dd:=4*a*c-b^2;
if dd<=0 then error "Form should be positive definite."; break; fi;
t1:={};
xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));
ylim:=ceil( 2*sqrt(a*M/dd));
for x from 0 to xlim do
for y from -ylim to ylim do
t2 := a*x^2+b*x*y+c*y^2;
if t2 <= M then t1:={op(t1),t2}; fi; od: od:
t3:=sort(convert(t1,list));
t4:=[];
for i from 1 to nops(t3) do
   if isprime(t3[i]) then t4:=[op(t4),t3[i]]; fi; od:
[[seq(t3[i],i=1..nops(t3))], [seq(t4[i],i=1..nops(t4))]];
end;
fd(1,1,10,500);

Mathematica

Module[{k, r}, Reap[For[k = 0, k <= 1000, k++, r = Reduce[k == x^2 + x y + 10 y^2, {x, y}, Integers]; If[r =!= False,(* Print[k," ",r]; *) Sow[k]]]][[2, 1]]] (* Jean-François Alcover, Mar 07 2023 *)