Strong normality and generalised Copeland--Erd\H{o}s numbers

TL;DR

This paper investigates the strong normality of certain Copeland-Erdős numbers and their extensions, showing that an infinite class of these numbers are not strongly normal, and discusses related open questions.

Contribution

It proves that infinitely many Copeland-Erdős and Bugeaud's Mahler-inspired numbers are not strongly normal, advancing understanding of their normality properties.

Findings

An infinite class of Copeland-Erdős numbers are not strongly normal.

Analogous non-normality results for Bugeaud's extensions.

Discussion of open questions on normality and strong normality.

Abstract

We prove that an infinite class of Copeland-Erd\H{o}s numbers are not strongly normal and provide the analogous result for Bugeaud's Mahler-inspired extension of the Copeland-Erd\H{o}s numbers. After the presentation of our results, we offer several open questions concerning normality and strong normality.