On the Sequentiality of the Successor Function

Abstract

Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy U -representation. The successor function maps the greedy U -representation of N onto the greedy U -representation of N +1. We characterize the sequences U such that the successor function associated with U is a left, resp. a right, sequential function. We also show that the odometer associated to U is continuous if and only if the successor function is right sequential.