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.

翻译：我们研究单词序列$(B_i)$的性质，其中$B_1 = 101$，对于$i \geq 1$，有$B_{i+1} = B_i C_i$，这里$C_i$是$B_i$去掉前$i$个符号后得到的序列。同时研究所有$B_i$均为其前缀的无穷二进制序列${\bf b} = 10101101011011101 \cdots$。我们证明$\bf b$是回归的，但非一致回归的；它具有指数级因子复杂度；它非形态的；且$1$的密度存在且为超越数。