Nice graphics, Patrick O'Neil!

> in general, it takes \$$2^n\$$ terms to go from 1/n to n/1.

> One natural question to ask is: "is \$$g\$$ surjective onto \$$\mathbb{Q}\$$?" I.e., for every \$$\frac{p}{q} \in \mathbb{Q}\$$, is there an \$$n \in \mathbb{N}\$$ such that \$$g(n) = \frac{p}{q}\$$?
Of course you mean not \$$\mathbb{Q}\$$ but the nonnegative rationals. This is a very interesting question.
What's the simplest nonnegative rational you can find that appears not to be of the form \$$g(n)\$$?