Absolutely abnormal, continued fraction normal numbers

TL;DR

This paper proves, assuming the Generalized Riemann Hypothesis, that there are numbers normal in continued fraction expansion but not in any base expansion, addressing a question in number theory.

Contribution

It provides a conditional proof of the existence of numbers with differing normality properties in continued fractions versus base expansions.

Findings

Conditional proof of continued fraction normality without base normality

Addresses a question posed by Bugeaud

Advances understanding of normality in different number representations

Abstract

In this short note, we give a proof, conditional on the Generalized Riemann Hypothesis, that there exist numbers x which are normal with respect to the continued fraction expansion but not to any base b expansion. This partially answers a question of Bugeaud.