PPL 098 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
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Prize Problem LedgerKimberling rewardsPPL 098Kimberling #11 · Run-length segment containment

Permanent problem IDPPL 098

Verified openIndependentconjecture

Combinatorics on words

Kimberling #11 · Run-length segment containment

For the unique nontrivial binary sequence s with s(1)=1 and r(r(s))=s, prove or disprove that every finite segment of its run-length sequence r(s) also occurs in s.

run lengthsbinary wordsinteger sequences
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The problem

For the unique nontrivial binary sequence s with s(1)=1 and r(r(s))=s, prove or disprove that every finite segment of its run-length sequence r(s) also occurs in s.

Open since1997original published problem
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$75Clark 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

3 unique reference linksSponsor’s live rewards page OEIS A025142 OEIS A025143
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