A243651 Nonnegative integers of the form x^2+11y^2.

0, 1, 4, 9, 11, 12, 15, 16, 20, 25, 27, 36, 44, 45, 47, 48, 49, 53, 60, 64, 69, 75, 80, 81, 92, 93, 99, 100, 103, 108, 111, 115, 121, 124, 125, 132, 135, 144, 148, 155, 163, 165, 169, 176, 177, 180, 185, 188, 192, 196, 199, 201, 207, 212, 213, 220, 225, 236, 240, 243, 256, 257, 267, 268, 269, 275

Offset: 0

Author

N. J. A. Sloane, Jun 08 2014

Keywords

• nonn

Comments

Discriminant -44.

Links

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

Crossrefs

Primes: A033209.

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(1,0,11,500);