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Distributions of Ulam Words up to Length 30

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arxiv 2410.01217 v2 pith:4GN3EUP2 submitted 2024-10-02 math.NT math.CO

Paul Adutwum , Hopper Clark , Ro Emerson , Alexandra (Sasha) Sheydvasser , Arseniy (Senia) Sheydvasser , Axelle Tougouma This is my paper · ORCID
classification math.NTmath.CO
keywords wordsbadelengthsomeulamableboundscomputed
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We further explore the notion of Ulam words considered by Bade, Cui, Labelle, and Li, giving some lower bounds on how many there are of a given length. Gaps between words and words of special type also reveal remarkable structure. By substantially increasing the number of computed terms, we are also able to sharpen some of the conjectures made by Bade et al.

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  1. Small gaps in the Ulam sequence

    math.CO 2025-01 conditional novelty 6.0 of 10

    For the Ulam sequence, this paper proves a_n <= 1.454^n for large n and proves that min_{1<=k<=n} a_{k+1}/a_k <= 1 + 7 log n / n for large n.

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