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

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Nonnegative integers of the form x3x^2+xy3xy+10y4y^2.

fd(13, 13, 104, 500);

Primes: A033227A106884.

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q

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

Discriminant -39.

N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

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);

Primes: A033227.

allocated for N. J. A. Sloane

q

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

0,2

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nonn

N. J. A. Sloane, Jun 08 2014

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allocated for N. J. A. Sloane

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