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

1,1

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

Prog

(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<b && gcd(a, c)==1, listput(L, [a, b, c]))
    )
  );
  Vec(L)
}
concat(concat(vector(30, a, pt60(a))))

Crossrefs

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

Sequence in context: A309419 A064540 A303276 * A335893 A199712 A173257

Adjacent sequences: A264823 A264824 A264825 * A264827 A264828 A264829

Keyword

nonn,tabf

Author

Colin Barker, Nov 26 2015

Status

approved