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An integer sequence $(a_n)_{n \in \mathbb{N}}$ is MC-finite if for every $m \ge 1$, the sequence $a_n \bmod m$ is eventually periodic. We discuss two methods for proving MC-finiteness: exhibiting a suitable recurrence relation, and the Specker–Blatter theorem. We also give an interesting example of an integer sequence $a_n$ such that $a_n \bmod m$ is eventually periodic iff $m$ is odd, namely the sequence A086714.