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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.
5
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
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
KEYWORD
nonn,tabf
AUTHOR
Colin Barker, Nov 26 2015
STATUS
approved