International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 525-528
Generalized Beatty sequences
Department of Mathematics and Statistics, University of Guelph, Ontario, Guelph NIG 2WI, Canada
Received 12 April 1978
Copyright © 1978 A. McD. Mercer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A well-known result due to . Beatty is that if and are positive irrational numbers satisfying then each positive integer is to be found in precisely one of the sequences , where denotes the integral part of . The present note generalizes this result to the case of the pair of sequences , with suitable hypotheses on the functions and . The special case , is the result due to Beatty.