After some time to think, yes, I'm pretty sure that it's all solutions. The shape of the function in the article means that there is only one b for any a. The formula I gave gives a solution, so it must be the solution. If you can find an n to generate an a, the formula must give you the correct b.

(As n goes from 0 to infinity, a goes from 1 to e, so the formula covers the entire range of possibilities.)

In my formula, however, n may be irrational, even for some rational a. I haven't proven that.