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Prize Problem LedgerKimberling rewardsPPL 108Kimberling #4 · A Hard Count

Permanent problem IDPPL 108

Verified openIndependentconjecture

Combinatorics

Kimberling #4 · A Hard Count

In Kimberling’s iterative counting process, prove or disprove that every positive integer is eventually written; the general form allows any finite positive initial count with distinct labels.

self-descriptive processinteger sequencesiteration
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The problem

In Kimberling’s iterative counting process, prove or disprove that every positive integer is eventually written; the general form allows any finite positive initial count with distinct labels.

Open since1998original published special case
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$100Clark 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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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