cp's OEIS Frontend

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

%I A244779 #13 Oct 31 2016 10:22:10
%S A244779 1,2,4,7,8,11,14,16,22,23,28,29,32,37,43,44,46,53,56,58,64,67,71,74,
%T A244779 77,79,86,88,92,106,107,109,112,113,116,121,127,128,134,137,142,148,
%U A244779 149,151,154,158,161,163,172,176,179,184,191,193,197,203,211,212,214
%N A244779 Positive numbers primitively represented by the binary quadratic form (1, 1, 2).
%C A244779 Discriminant = -7.
%H A244779 Robert Israel, <a href="/A244779/b244779.txt">Table of n, a(n) for n = 1..10000</a>
%H A244779 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)
%p A244779 PriRepBQF := proc(a, b, c, n) local L,q,R,r,k;
%p A244779 q := a*x^2 + b*x*y + c*y^2; L := NULL;
%p A244779 for k from 1 to n do
%p A244779    R := [isolve(q = k)];
%p A244779    if R = [] then next fi;
%p A244779    for r in R do
%p A244779       igcd(op(2,r[1]), op(2,r[2]));
%p A244779       if 1 = % then L := L,k; break fi od
%p A244779 od; L end:
%p A244779 A244779_list := n -> PriRepBQF(1, 1, 2, n); A244779_list(214);
%p A244779 # Alternate program
%p A244779 A244779_set:= proc(N) local A, B, y,x;
%p A244779    A:= {};
%p A244779    for y from 0 to floor(sqrt(4*N/7)) do
%p A244779      for x from ceil(-y/2) to floor(-y/2 + sqrt(N - 7/4*y^2)) do
%p A244779        if igcd(x,y) = 1 then
%p A244779          A:= A union {x^2 + x*y + 2*y^2}
%p A244779        fi
%p A244779      od
%p A244779     od;
%p A244779 A
%p A244779 end proc:
%p A244779 A244779_set(1000); # _Robert Israel_, Jul 06 2014
%t A244779 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 *)
%Y A244779 Cf. A244780, A244819.
%K A244779 nonn
%O A244779 1,2
%A A244779 _Peter Luschny_, Jul 06 2014