A243652 Nonnegative integers of the form 2x^2+xy+6y^2.

0, 2, 6, 7, 8, 9, 12, 16, 18, 21, 24, 27, 28, 32, 34, 36, 42, 48, 50, 51, 53, 54, 56, 59, 61, 63, 64, 68, 72, 74, 81, 84, 89, 94, 96, 97, 98, 102, 108, 111, 112, 119, 126, 128, 131, 136, 142, 144, 147, 148, 150, 153, 157, 158, 159, 162, 166, 168, 173, 175, 177, 183, 189, 192, 196, 200, 202, 204, 206

Offset

0,2

Comments

Discriminant -47.

Links

Table of n, a(n) for n=0..68.

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(2, 1, 6, 500);

Crossrefs

Primes: 106898.

Sequence in context: A184939 A043050 A159843 * A080780 A138168 A047279

Adjacent sequences: A243649 A243650 A243651 * A243653 A243654 A243655

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2014

Status

approved