Evidently, the weird number 13 turning up in the definition of this function is just so there's 3 extra digits, in addition to the 10 decimal ones. But 10 itself sure is pretty arbitrary here, and just used for human-habit reasons?
If we mapped, instead of base-10, simply to base-2, we would only need base-5 as input, and the analogue construction would sure work as well. That would look a bit less "magic-number"-like.
Or am I mistaken here? What might perhaps not work?