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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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. A229849, A229858, A229859, A264826.

Sequence in context: A151548 A256258 A177433 * A214091 A071581 A184722

Adjacent sequences:  A264824 A264825 A264826 * A264828 A264829 A264830

KEYWORD

nonn,tabf

AUTHOR

Colin Barker, Nov 26 2015

STATUS

approved

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Last modified November 14 19:59 EST 2019. Contains 329128 sequences. (Running on oeis4.)