Abstract:

Suppose $c\geq 2$ and $d\geq 2$ are integers, and let $S$ be the set of integers $\left\lfloor c^j/d^k\right\rfloor$, where $j$ and $k$ range over the nonnegative integers. Assume that $c$ and $d$ are multiplicatively independent; that is, if $p$ and $q$ are integers for which $c^p=d^q,$ then $p=q=0$. The numbers in $S$ form interspersions in various ways. Related fractal sequences and permutations of the set of nonnegative integers are also discussed.