PPL 106 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
Prize Problem LedgerPPL · Open reward indexAll 177 problems
Prize Problem LedgerKimberling rewardsPPL 106Kimberling #2 · Does the Kimberling sequence contain every integer?

Permanent problem IDPPL 106

Verified openIndependentconjecture

Number theory

Kimberling #2 · Does the Kimberling sequence contain every integer?

Prove or disprove that every positive integer occurs in the sequence beginning 1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, 14, 28, ….

integer sequencessurjectivityrecurrence
01

The problem

Prove or disprove that every positive integer occurs in the sequence beginning 1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, 14, 28, ….

Open since1991original published problem
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01$300Clark 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 ↗
03

Sources & reading

1 unique reference linksSponsor’s live rewards page
04

Related open targets

Number theoryBeal conjecturePPL 005 · $1,000,000 · 33 years openNumber theoryBirch–Swinnerton-Dyer conjecturePPL 006 · $1,000,000 · 61 years openNumber theoryRiemann hypothesisPPL 138 · $1,000,000 · 167 years open