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Is the following sequence always periodical?

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    $\begingroup$ Unlikely. If $M>10^6$, then it is very rare that a number with $M$ digits is divisible by $M$. So in average you are multiplying more often than dividing, if the starting $n$ is large enough. $\endgroup$
    – Chris Wuthrich
    Commented Dec 28, 2021 at 0:17

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