On the Sequentiality of the Successor Function

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 to 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.