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A244779 Positive numbers primitively represented by the binary quadratic form (1, 1, 2). 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 24 13:06 EDT 2021. Contains 348231 sequences. (Running on oeis4.)