标题： 逗号序列在其他进制中是有限的 显示英文标题

标题： The Comma Sequence is Finite in Other Bases

摘要： 逗号序列(1, 12, 35, 94, ...)是字典序最早的序列，使得相邻项的差等于分隔它们的逗号两侧数字的连接。 "广义逗号序列"的行为取决于数字所使用的基数以及序列的初始值。 我们提供了一个计算证明，表明所有基数3到633之间的逗号序列都是有限的。 依赖于一个组合猜想，Angelini等人估计基数b的逗号序列的最后一个元素应该大约是exp(O(b))。 我们证明了他们的猜想，但提供了证据表明正确的估计实际上是exp(O(b log b))。 显示英文摘要

摘要： The comma sequence (1, 12, 35, 94, ...) is the lexicographically earliest sequence such that the difference of consecutive terms equals the concatenation of the digits on either side of the comma separating them. The behavior of a "generalized comma sequence" depends on the base the numbers are written in, as well as the sequence's initial values. We provide a computational proof that all comma sequences in bases 3 through 633 are finite. Relying on a combinatorial conjecture, Angelini et al. estimated that the final element of a comma sequence in base b should be roughly exp(O(b)). We prove their conjecture, but provide evidence that the correct estimate is actually exp(O(b log b)).