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 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. (C) 1997 Academic Press.