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

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.