OFFSET
1,1
REFERENCES
Ross Honsberger, "Mathematical Delights", MAA, 2004, p. 64.
LINKS
Park City Mathematics Institute, Session 13 Number Theory, Summer 2001. A similar factoring allows for the generation of Eisenstein triples, which are numbers that form the sides of a triangle with a 60-degree angle.
FORMULA
T(n) = {a(n), b(n), c(n)} such that a(n)^2 + b(n)^2 - a(n)*b(n) - c(n)^2 = 0 and abs(a(n) - b(n)) > 0.
EXAMPLE
Grouped as threes: {{3, 8, 7}, {5, 8, 7}, {5, 21, 19}, {6, 16, 14}, {7, 15, 13}, {8, 3, 7}, {8, 5, 7}, {8, 15, 13}, {9, 24, 21}, {10, 16, 14}, {15, 7, 13}, {15, 8, 13}, {15, 24, 21}, {16,6, 14}, {16, 10, 14}, {16, 21, 19}, {21, 5, 19}, {21, 16, 19}, {24, 9, 21}, {24, 15, 21}}
MATHEMATICA
f[a_, b_, c_] = If[c^2 - a^2 - b^2 + a*b == 0 && Abs[a - b] > 0, {a, b, c}, {}] a0 = Flatten[Delete[Union[Table[Delete[Union[Table[Flatten[Table[f[a, b, c], {c, 1, 25}]], {b, 1, 25}]], 1], {a, 1, 25}]], 1], 1] b0 = Sort[a0] Flatten[b0]
CROSSREFS
KEYWORD
nonn,tabf,uned
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 10 2006
STATUS
approved