Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence
Kohta Gejima, Fumichika Takamizo
Published: 2025/9/26
Abstract
We prove that the sequence of the last nonzero digits of factorials in every integer base $b>2$ is not eventually periodic. We also extend the Adamczewski--Bugeaud criterion, originally formulated for integer base expansions, to Cantor base expansions associated with a periodic Cantor base. As an application, we show that a certain real number expressed through a Cantor base expansion is transcendental when the Cantor base and the digit sequence satisfy suitable conditions.