paper

An arithmetical excursion via Stoneham numbers

arXiv:1212.3449 · doi:10.1017/S1446788713000682

Abstract

Let $p$ be a prime and $b$ a primitive root of $p^{2}$ . In this paper, we give an explicit formula for the number of times a value in $0, 1, ..., b - 1$ occurs in the periodic part of the base $b$ expansion of $1/ p^{m}$ . As a consequence of this result, we prove two recent conjectures of Francisco AragÃ³n, Daivd Bailey, Jonathan Borwein, and Peter Borwein concerning the base $b$ expansion of Stoneham numbers.

12 pages