Rollerblades, Basketball... I'm lovin' it

We had a speaker come and give a talk yesterday - Patrick Dorey, from University of Durham - and the talk was extremely interesting; it was actually on a subject upon which I "work", namely integrable systems. However, incidentally, in the course of his talk, he mentioned how the subject related to a famous problem in mathematics called "the McNugget Problem."

McDonald's (used to) serve McNuggets (R) in only three sizes - 6, 9, and 20. The question then naturally arises as to whether you can order ANY number of nuggets (quickly answered in the negative - try to order 3 McNuggets) and if not, precisely which numbers are disallowed?

It turns out that, because the three numbers are relatively prime (i.e., the only number by which you can divide all three numbers is 1), if you want a large enough number of McNuggets, you will eventually be accommodated. Turns out, the largest "McNugget number" is 43 - you will unfortunately be unable to order 43 McNuggets, but ANY number higher than that, and you're golden (arches). The other McNugget numbers are:

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, and 37.

Of course, McDonald's (partially) realized the error of their weighs, and have expanded the options. McNuggets now come in 4,6, and 10 piece boxes, and if you include the Chicken Selects (R) Premium Breast Strips (offered in 3 and 5 piece sets) you can now get any number of chicken pieces other than 1 and 2. But dang-it, I only WANT 2!