A243653 Nonnegative integers of the form 3x^2+xy+4y^2.

0, 3, 4, 6, 8, 12, 14, 16, 17, 18, 21, 24, 27, 28, 32, 34, 36, 37, 42, 48, 49, 54, 56, 63, 64, 68, 71, 72, 74, 75, 79, 81, 84, 96, 98, 100, 101, 102, 103, 106, 108, 112, 118, 119, 122, 126, 128, 136, 141, 142, 144, 147, 148, 149, 150, 153, 158, 159, 162, 168, 177, 178, 183, 188, 189, 192, 194, 196

Offset

0,2

Comments

Discriminant -47.

Links

Robert Israel, Table of n, a(n) for n = 0..9999

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(3, 1, 4, 500);
# Alternative:
select(t -> nops([isolve(3*x^2+x*y+4*y^2=t)])>0, [$0..1000]); # Robert Israel, Jun 08 2014

Mathematica

sol[t_] := Solve[3 x^2 + x y + 4 y^2 == t, {x, y}, Integers];
Select[Range[0, 1000], sol[#] != {}&] (* Jean-François Alcover, Jul 28 2020 *)

Crossrefs

Primes: A106895.

Sequence in context: A167711 A037346 A250122 * A365168 A203444 A008864

Adjacent sequences: A243650 A243651 A243652 * A243654 A243655 A243656

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2014

Status

approved