3 problems

Let $S$ be a finite set of primes, let $b\geq 2$ satisfy $\#(S\cup F_b)>1$, and let $M_S$ denote the set of nodes associated with $S$. If a node $m\in M_S$ has a $b$-ary expansion…

Fix a base $b\geq 2$. The Liouville word is the infinite word whose $i!$-th digit is $1$ and whose other digits are $0$. A word is finite factorial if it satisfies the finite facto…

Let $b\geq 2$ be a base. A number is partially finite factorial if it has a $b$-ary expansion satisfying the partially finite factorial property defined in the source. The partial…