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

0,3

Comments

Discriminant -44.

Links

Table of n, a(n) for n=0..65.

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

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);

Crossrefs

Primes: A033209.

Sequence in context: A000974 A291626 A312833 * A292673 A035233 A341788

Adjacent sequences: A243648 A243649 A243650 * A243652 A243653 A243654

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2014

Status

approved