A244779 Positive numbers primitively represented by the binary quadratic form (1, 1, 2).

1, 2, 4, 7, 8, 11, 14, 16, 22, 23, 28, 29, 32, 37, 43, 44, 46, 53, 56, 58, 64, 67, 71, 74, 77, 79, 86, 88, 92, 106, 107, 109, 112, 113, 116, 121, 127, 128, 134, 137, 142, 148, 149, 151, 154, 158, 161, 163, 172, 176, 179, 184, 191, 193, 197, 203, 211, 212, 214

Offset

1,2

Comments

Discriminant = -7.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Maple

PriRepBQF := proc(a, b, c, n) local L, q, R, r, k;
q := a*x^2 + b*x*y + c*y^2; L := NULL;
for k from 1 to n do
   R := [isolve(q = k)];
   if R = [] then next fi;
   for r in R do
      igcd(op(2, r[1]), op(2, r[2]));
      if 1 = % then L := L, k; break fi od
od; L end:
A244779_list := n -> PriRepBQF(1, 1, 2, n); A244779_list(214);
# Alternate program
A244779_set:= proc(N) local A, B, y, x;
   A:= {};
   for y from 0 to floor(sqrt(4*N/7)) do
     for x from ceil(-y/2) to floor(-y/2 + sqrt(N - 7/4*y^2)) do
       if igcd(x, y) = 1 then
         A:= A union {x^2 + x*y + 2*y^2}
       fi
     od
    od;
A
end proc:
A244779_set(1000); # Robert Israel, Jul 06 2014

Mathematica

Reap[For[n = 1, n < 1000, n++, r = Reduce[x^2 + x y + 2 y^2 == n, {x, y}, Integers]; If[r =!= False, If[AnyTrue[{x, y} /. {ToRules[r /. C[1] -> 0]}, CoprimeQ @@ # &], Sow[n]]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)

Crossrefs

Cf. A244780, A244819.

Sequence in context: A080704 A316094 A290259 * A162158 A018552 A030773

Adjacent sequences: A244776 A244777 A244778 * A244780 A244781 A244782

Keyword

nonn

Author

Peter Luschny, Jul 06 2014

Status

approved