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

Volume 191 / 2019

Bartosz Sobolewski Acta Arithmetica 191 (2019), 173-189 MSC: Primary 11A63; Secondary 11B05, 11B85, 68Q45, 68R15. DOI: 10.4064/aa180630-29-1 Published online: 23 August 2019


We study the sequence describing the last block of $k$ digits in the base-$b$ expansion of $n!$ not ending with $0$. We determine for which $b$ this sequence is automatic and show how to generate it using a uniform morphism. We also compute how often this sequence attains each possible value.


  • Bartosz SobolewskiInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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