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Prize Problem LedgerKimberling rewardsPPL 102Kimberling #13.3 · Positive d-values recur within three steps

Permanent problem IDPPL 102

Verified openIndependentconjecture

Combinatorics

Kimberling #13.3 · Positive d-values recur within three steps

Prove or refute that whenever d(k)>0, at least one of d(k+1), d(k+2), or d(k+3) is positive.

self-generated sequencesinteger sequencesrecurrence
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The problem

Prove or refute that whenever d(k)>0, at least one of d(k+1), d(k+2), or d(k+3) is positive.

Open since2007sequence-record date
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$25 proof · $20 counterexampleClark 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. Each of the four propositions has its own $25 proof / $20 counterexample offer.

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

Award source ↗
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Sources & reading

3 unique reference linksSponsor’s live rewards page OEIS A131388 OEIS A131389
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Related open targets

CombinatoricsErdős Problem #20PPL 049 · $1000 · 66 years openCombinatoricsErdős Problem #161PPL 046 · $500 · 36 years openNumber theoryKimberling #2 · Does the Kimberling sequence contain every integer?PPL 106 · $300 · 35 years open