Automaticity of the sequence of the last nonzero digits of n! in a fixed base
Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 283-291.

En 2011, Deshouillers et Ruzsa [5] ont donné des arguments en faveur de la non-automaticité de la suite des derniers chiffres non nuls de n! en base 12. Cette assertion a été prouvée quelques années plus tard par Deshoulliers [4]. Dans cet article, nous donnons une preuve alternative qui nous permet de généraliser le problème et donner une caractérisation complète des bases pour lesquelles la suite des derniers chiffres non nuls de n! est automatique.

In 2011 Deshouillers and Ruzsa [5] tried to argue that the sequence of the last nonzero digit of n! in base 12 is not automatic. This statement was proven a few years later by Deshoulliers in [4]. In this paper we provide an alternate proof that lets us generalize the problem and give an exact characterization of the bases for which the sequence of the last nonzero digits of n! is automatic.

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DOI : https://doi.org/10.5802/jtnb.1080
Classification : 11B85,  11A63,  68Q45,  68R15
Mots clés : automatic sequence, factorial, the last nonzero digit
@article{JTNB_2019__31_1_283_0,
     author = {Eryk Lipka},
     title = {Automaticity of the sequence of the last nonzero digits of $n!$ in a fixed base},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {283--291},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {1},
     year = {2019},
     doi = {10.5802/jtnb.1080},
     zbl = {07246525},
     mrnumber = {3994731},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1080/}
}
Eryk Lipka. Automaticity of the sequence of the last nonzero digits of $n!$ in a fixed base. Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 1, pp. 283-291. doi : 10.5802/jtnb.1080. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1080/

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