Normality in Pisot Numeration Systems

TL;DR

This paper generalizes a known result about the normality of concatenated primes in base 10 to Pisot number bases where all integers have finite expansions, expanding understanding of normality in different numeration systems.

Contribution

The paper extends the normality result from base 10 to Pisot bases with finite expansions for all integers, broadening the scope of normality in numeration systems.

Findings

Concatenation of primes in Pisot bases yields normal numbers.

Normality result previously known for base 10 is generalized.

Supports broader classes of bases with finite expansions.

Abstract

Copeland and Erd\H{o}s showed that the concatenation of primes when written in base $10$ yields a real number that is normal to base $10$. We generalize this result to Pisot number bases in which all integers have finite expansion.