Brik's sequence: a strange recursion
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909025931624448 |
|---|---|
| author | Shallit, Jeffrey |
| author_facet | Shallit, Jeffrey |
| contents | We study the properties of the sequence of words $(B_i)$, where $B_1 = 101$ and $B_{i+1} = B_i C_i$ for $i \geq 1$, where $C_i$ is $B_i$ with the first $i$ symbols removed, and the infinite binary sequence ${\bf b} = 10101101011011101 \cdots$ of which all the $B_i$ are prefixes. We show that $\bf b$ is recurrent, but not uniformly recurrent; it has exponential factor complexity; it is not morphic; and the density of $1$'s exists and is transcendental. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brik's sequence: a strange recursion Shallit, Jeffrey Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory We study the properties of the sequence of words $(B_i)$, where $B_1 = 101$ and $B_{i+1} = B_i C_i$ for $i \geq 1$, where $C_i$ is $B_i$ with the first $i$ symbols removed, and the infinite binary sequence ${\bf b} = 10101101011011101 \cdots$ of which all the $B_i$ are prefixes. We show that $\bf b$ is recurrent, but not uniformly recurrent; it has exponential factor complexity; it is not morphic; and the density of $1$'s exists and is transcendental. |
| title | Brik's sequence: a strange recursion |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory |
| url | https://arxiv.org/abs/2605.07542 |