On the number of multi-base representations of an integer
Daniel Krenn, Dimbinaina Ralaivaosaona, Stephan G. Wagner · 2014
Abstract. In a multi-base representation of an integer (in contrast to, for example, the binary or decimal representation) the base (or radix) is replaced by products of powers of single bases. The resulting numeral system is usually redundant, which means that each integer can have multiple different digit expansions. We provide a general asymptotic formula for the number of such multi-base representations of a positive integer n. Moreover, we prove central limit theorems for the sum of digits and the Hamming weight of a random representation. 1.