User blog comment:Testitemqlstudop/On mapping positive integers to ordinals/@comment-43798125-20191027101113/@comment-44130370-20191028024120

It would most definitely be hard to make it 1to1. If to evaluate ord(n), you need to first evaluate ord(n-1), ord(n-2), ord(n-3), ... it creates an exponential blowup in the evaulation complexity. Note that you can't (?) employ a DP approach here since ord(n-2) changes if ord(n-3) changes.

If somehow your method allowed a memoizaiton approach, it will still border on O(n^2) or O(n^3) amortized while mine is O((log n)^2)