On the last nonzero digits of $n!$ in a given base

Abstract

In this paper we study the sequence of strings of $k$ last nonzero digits of $n!$ in a given base $b$. We determine for which $b$ this sequence is automatic and show how to generate it using a uniform morphism. We also compute how often each possible string of $k$ digits appears as the $k$ last nonzero digits of $n!$.