[pmiller2]

Try the inverse Ackerman function instead: https://en.m.wikipedia.org/w/index.php?title=Ackermann_funct...

If non-computable functions are on the table, define f(n) to be the smallest k such that BB-k >= n, where BB-n is the n-th Busy Beaver number: https://en.wikipedia.org/wiki/Busy_beaver

Edit: looks like @tromp managed to reply before I added the bit about BB-n. :-)

[tromp]

Or the inverse TREE() function [1]. There's also the inverse Busy Beaver function if you don't insist on computability...

[1] https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#TREE(...

[btilly]

Non-computable functions are indeed on the table as long as they tend to infinity in the limit..at the cost that figuring out when you start to hit that limit is undoubtably itself non-computable.