The minimal growth of a \(k\)-regular sequence

Authors

  • J. P. Bell University of Waterloo
  • M. Coons University of Newcastle
  • K. G. Hare University of Waterloo

Keywords:

Automata sequences, regular sequences, growth of arithmetic function

Abstract

We determine a lower gap property for the growth of an unbounded \(\mathbb{Z}\)-valued \(k\)-regular sequence. In particular, if \(f:\mathbb{N}\to\mathbb{Z}\) is an unbounded \(k\)-regular sequence, we show that there is a constant \(c>0\) such that \(|f(n)|>c\log n\) infinitely often. We end our paper by answering a question of Borwein, Choi, and Coons on the sums of completely multiplicative automatic functions. DOI: 10.1017/S0004972714000197

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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