# nt.number theory – Reference request for Additive persistence of a number

It is well known fact that each natural number can be represented uniquely in any base. So we can define digit sum function whose value is sum of digits of the natural number in given base.

Let $$f(n,b)$$ be digit sum of n in base b. It is very easy to prove that for each n in natural number there exist a k such that $$f^k(n,b)$$ (function composition) is a digit in base $$b$$. The smallest such $$k$$ is called additive persistence of $$n$$.

Where I can find the research articles published on these topics? I am able to only find few articles in Research Gate and few other websites. Can you give references where this additive persistence is used or its properties are discussed?