A264827 (a,b,c) in lexicographic order such that a^2 + b^2 + a*b - c^2 = 0 with a < b < c and gcd(a, b) = 1.

3, 5, 7, 5, 16, 19, 7, 8, 13, 7, 33, 37, 9, 56, 61, 11, 24, 31, 11, 85, 91, 13, 35, 43, 13, 120, 127, 15, 161, 169, 16, 39, 49, 17, 63, 73, 17, 208, 217, 19, 80, 91, 19, 261, 271, 21, 320, 331, 23, 120, 133, 23, 385, 397, 24, 95, 109, 25, 143, 157

Offset

1,1

Comments

The sides of a primitive 120-degree integer triangle.

Links

Colin Barker, Table of n, a(n) for n = 1..9999

Wikipedia, Eisenstein triple

Example

Triples (a,b,c) begin:
  3,  5,  7;
  5, 16, 19;
  7,  8, 13;
  7, 33, 37;
  9, 56, 61;
  ...

Prog

(PARI)
pt120(a) = {
  my(L=List(), n=-3*a^2, f, g, b, c);
  fordiv(n, f,
    g=n\f;
    if(f>g && (g+f)%2==0 && (f-g)%4==0,
      c=(f-g)\4; b=((f+g)\2-a)\2;
      if(b>0 && a<b && gcd(a, b)==1, listput(L, [a, b, c]))
    )
  );
  Vec(L)
}
concat(concat(vector(30, a, pt120(a))))

Crossrefs

Cf. A002476, A229849, A229858, A229859, A264826.

Sequence in context: A151548 A256258 A177433 * A214091 A353905 A340665

Adjacent sequences: A264824 A264825 A264826 * A264828 A264829 A264830

Keyword

nonn,tabf

Author

Colin Barker, Nov 26 2015

Status

approved