PPL 107 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
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Prize Problem LedgerKimberling rewardsPPL 107Kimberling #23 · Special linearly recurrent Beatty subsequences

Permanent problem IDPPL 107

Verified openIndependentconjecture

Number theory

Kimberling #23 · Special linearly recurrent Beatty subsequences

Characterize the real numbers r for which the Beatty sequence floor(nr) contains a homogeneous linearly recurrent subsequence.

Beatty sequenceslinear recurrencesDiophantine approximation
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The problem

Characterize the real numbers r for which the Beatty sequence floor(nr) contains a homogeneous linearly recurrent subsequence.

Open sinceUnknowndate not stated by sponsor
Last checked2026.07.27Catalog verification
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Reward offers

Offer 01$50Clark Kimberling
Personal offer

Be first to publish a solution in a refereed journal, or submit a short proof that Kimberling accepts as correct and complete. For solutions after 1 January 2025, Kimberling says the stated amount will be donated in the solver’s name to the Online Encyclopedia of Integer Sequences; it is not direct cash to the solver.

Current post-2025 form: a donation to OEIS in the solver’s name.

Award source ↗
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Sources & reading

1 unique reference linksSponsor’s live rewards page
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