Check out https://en.wikipedia.org/wiki/Kaprekar%27s_routine https://en.wikipedia.org/wiki/Kaprekar%27s_routine At a glance, there seem to be some patterns, li

Check out https://en.wikipedia.org/wiki/Kaprekar%27s_routine https://en.wikipedia.org/wiki/Kaprekar%27s_routine At a glance, there seem to be some patterns, like how for those bases with a 2-digit Kaprekar number the sum of the digits is base-1. There must be some number theory explanation for it.