A243681 Nonnegative integers of the form 3x^2+3xy+4y^2.

0, 3, 4, 10, 12, 13, 16, 22, 25, 27, 30, 36, 40, 48, 52, 55, 61, 64, 66, 75, 79, 82, 88, 90, 94, 100, 108, 117, 118, 120, 121, 127, 129, 130, 142, 144, 147, 156, 160, 165, 166, 172, 178, 192, 196, 198, 199, 205, 208, 211, 220, 225, 235, 243, 244, 246, 250, 256, 264, 270, 274, 282, 283, 286, 295, 298

Offset

0,2

Comments

Discriminant -39.

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(3, 3, 4, 500);

Mathematica

Take[Union[3First[#]^2+3(Times@@#)+4Last[#]^2&/@Tuples[Range[-10, 10], 2]], 70] (* Harvey P. Dale, Jul 25 2014 *)

Crossrefs

Primes: A106884.

Sequence in context: A079353 A242654 A370860 * A242881 A287448 A325235

Adjacent sequences: A243678 A243679 A243680 * A243682 A243683 A243684

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2014

Status

approved