Three-dimensional triangle of one less than the conductor of a, b and c for the expression a*x + b*y + c*z.

1, 1, 3, 2, 1, 0, 5, 3, 7, 7, 1, 5, 5, 3, 4, 6, 5, 11, 9, 9, 1, 0, 5, 3, 7, 11, 0, 13, 0, 9, 5, 5, 17, 11, 17, 1, 7, 5, 3, 7, 11, 7, 0, 11, 13, 5, 11, 10, 13, 17, 7, 13, 23, 12, 19, 20, 1, 0, 5, 3, 7, 11, 0, 17, 0, 19, 5, 11, 13, 23, 15, 0, 7, 0, 27, 0, 19, 7, 17, 15, 31, 23, 22, 31

4

We assume 1 < a < b < c. This is the greatest k such that a*x + b*y + c*z does not equal k for any nonnegative x, y, and z. The numbers x, y, and z are assumed to be nonnegative.

T. D. Noe, Plot of rows 4 to 40

T. D. Noe, Table of rows 4 to 40

David Bessoud and Stan Wagon, A Course in Computational Number Theory, Key College Publishing, 2000.

(Mma) Needs["CNT`”]; nn = 10; Table[d = Conductor[{a, b, c}] - 1; If[d == Infinity, d = 0]; d, {c, 4, nn}, {b, 3, c - 1}, {a, 2, b - 1}]

Cf. S000429, S000430, S000431, S000433.

nonn,tabf

T. D. Noe, Dec 24 2014