6 problems

Let $(a_n)$ be a sequence satisfying Benford's Law through equidistribution dynamics, and suppose the continued fraction of its rotation number is of bounded type, meaning that…

Let $b$ range over integer bases greater than $1$. A base is B-EQUI-PERS at sample size $N$ when there exists a continued-fraction convergent denominator $q_k\leq N$ such that…

Let $\mathfrak{B}_0\supset \mathfrak{B}_1\supset\cdots$ be an $m$-dimensional linear-fragmentation process, and for $1\leq d\leq m$ let $\mathfrak{m}_d^{(N)}$ denote the maximum pr…

Let $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime, and let $P(d)$ denote the Benford probability of leading digit $d$. The waiting time between successive occurrences of a leadi…

Let $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime, and consider the leading digits of consecutive terms $M_n,M_{n+1},\ldots,M_{n+k-1}$. A digit is Benford-distributed when its p…

Let $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime, let $D(M_n)$ denote the leading digit of $M_n$, and define the Benford error by … Here $P(d)$ is the Benford probability of th…