Can any periodic set of integers be realized as the zero-set of a linear recurrence relation? It's stated on the OEIS page for eventually periodic sequences that "all eventually periodic sequences with period N are linear recurrence relations of order at most N" but if you interpret "are linear recurrence relations" as being the zero set of a linear recurrence relation this statement can't be true because Skolem-Mahler-Lech gives a stronger characterization than just eventually periodic (the zero-set must include every earlier member of the residue classes in the periodic part too). At the moment I don't see an obvious way to do it for periodic sets and can't find any other mention online
2026-02-23 07:40:34.1771832434
Skolem-Mahler-Lech Converse
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