I'm doing a presentation on Godel's paper "What Is Cantor's Continuum Problem?", and would like to include a computational demonstration of the countability of the algebraic numbers.
I'm looking for an explicit bijection $f : \mathbb{N} \rightarrow \mathbb{A}$ from the natural to algebraic numbers (preferably such that $f(n)$ is relatively swiftly computable).
The plan is to code up an algorithm based on this bijection and run it during the talk, spewing out a non-repeating sequence of algebraic numbers for 50 minutes. It's of course not a proof of countability, just a demo. I'm assuming that it will be similar in construction to the "zig-zag" bijection $\mathbb{N} \rightarrow \mathbb{Q}$.
Thanks in advance!