当前位置: X-MOL 学术arXiv.cs.FL › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The Look-and-Say The Biggest Sequence Eventually Cycles
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2020-06-12 , DOI: arxiv-2006.07246
\'Eric Brier and R\'emi G\'eraud-Stewart and David Naccache and Alessandro Pacco and Emanuele Troiani

In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and $a$ is the maximum of $b$ and the run's length. We dub this the "look-and-say the biggest" (LSB) sequence. Conway's sequence is very similar ($b$ is just the run's length). For any starting value except 22, Conway's sequence grows exponentially: the ration of lengths converges to a known constant $\lambda$. We show that LSB does not: for every starting value, LSB eventually reaches a cycle. Furthermore, all cycles have a period of at most 9.

中文翻译:

最大的序列最终循环

在本文中,我们考虑 Conway 序列的变体(OEIS A005150,A006715),定义如下:序列中的下一项是通过考虑连续运行的数字获得的,并将它们重写为 $ab$,其中 $b$ 是数字, $a$ 是 $b$ 和运行长度的最大值。我们将其称为“外观最大”(LSB) 序列。Conway 的序列非常相似($b$ 只是运行的长度)。对于除 22 以外的任何起始值,康威序列呈指数增长:长度比收敛到一个已知常数 $\lambda$。我们证明 LSB 不会:对于每个起始值,LSB 最终都会达到一个循环。此外,所有循环的周期最多为 9。
更新日期:2020-06-15
down
wechat
bug