A264826 Primitive Eisenstein triples: (a,b,c) in lexicographic order such that a^2 + b^2 - a*b - c^2 = 0, a < b < c, and gcd(a, b) = 1.

3, 7, 8, 5, 7, 8, 5, 19, 21, 7, 13, 15, 7, 37, 40, 8, 13, 15, 9, 61, 65, 11, 31, 35, 11, 91, 96, 13, 43, 48, 13, 127, 133, 15, 169, 176, 16, 19, 21, 16, 49, 55, 17, 73, 80, 17, 217, 225, 19, 91, 99, 19, 271, 280, 21, 331, 341, 23, 133, 143, 23, 397, 408

Offset: 1

Author

Colin Barker, Nov 26 2015

Keywords

• nonn
• tabf

Comments

The sides of a primitive 60-degree integer triangle.

Links

• Colin Barker, Table of n, a(n) for n = 1..9999
• Eric Weisstein's World of Mathematics, Pythagorean Triple
• Wikipedia, Eisenstein triple

Crossrefs

Cf. A089025, A121992, A201223, A263728, A264827.

Programs

PARI

pt60(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,
      b=(f-g)\4; c=((f+g)\2+a)\2;
      if(c>0 && a