Positional number systems with digits forming an arithmetic progression
In this paper a number system that arises in a natural way in a graph-theoretic context is studied. It is defined by a set of positive digits forming an arithmetic progression and complete residue system modulo the base \(b\) The question how the digits are distributed among the first \(N\) integers is addressed. The authors give an explicit formula for the length of the representation and a explicit formula that gives the \(j\)th digit of the representation of \(n\). A Delange type analysis of the frequencies of digits is based upon such an explicit formula. They also study the averages and obtain asymptotic results involving periodic functions that are completely described via their Fourier coefficients. The Mellin-Perron approach is used.
scientific article; zbMATH DE number 5567006