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An integer sequence \((a_n)_{n \in \mathbb {N}}\) is MC-finite if for all m, the sequence \(a_n \bmod m\) is eventually periodic. There are MC-finite sequences \((a_n)_{n \in \mathbb {N}}\) such that the function \(F: (m,n) \mapsto a_n \bmod m\) is not computable. In Filmus et al. (2023) [3] we presented concrete examples of MC-finite sequences taken from the Online Encyclopedia of Integer Sequences (OEIS) without discussing the computability of F. In this paper we discuss cases when this F is effectively computable.

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Effective MC-Finiteness

  • 章节

  • 发表日期：

    2026年

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  • Yuval Filmus,
  • Eldar Fischer,
  • Johann A. Makowsky

摘要

An integer sequence \((a_n)_{n \in \mathbb {N}}\) is MC-finite if for all m, the sequence \(a_n \bmod m\) is eventually periodic. There are MC-finite sequences \((a_n)_{n \in \mathbb {N}}\) such that the function \(F: (m,n) \mapsto a_n \bmod m\) is not computable. In Filmus et al. (2023) [3] we presented concrete examples of MC-finite sequences taken from the Online Encyclopedia of Integer Sequences (OEIS) without discussing the computability of F. In this paper we discuss cases when this F is effectively computable.