论文标题
看起来最大的序列最终循环
The Look-and-Say The Biggest Sequence Eventually Cycles
论文作者
论文摘要
在本文中，我们考虑了Conway序列的变体（OEI A005150，A006715）定义如下：该序列中的下一个术语是通过考虑连续的数字来获得的，并将其重写为$ ab $，其中$ b $是$ b $是数字，$ $ a $是$ b $ and $ b $和运行的长度。我们将其列为“外观和最大”（LSB）序列。康威的序列非常相似（$ b $只是运行的长度）。对于除22以外的任何起始值，康威的序列呈指数增长：长度的分级收敛到已知常数$λ$。我们表明LSB并非：对于每个起始值，LSB最终都达到了一个周期。此外，所有周期最多都有9个周期。
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 $λ$. 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.
