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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 08 2014
STATUS
approved