International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1978 / Article

Open Access

Volume 1 |Article ID 284925 | 4 pages | https://doi.org/10.1155/S0161171278000514

Generalized Beatty sequences

Received12 Apr 1978

Abstract

A well-known result due to S. Beatty is that if α and β are positive irrational numbers satisfying α1+β1=1 then each positive integer is to be found in precisely one of the sequences {[kα]}, {[kβ]}(k=1,2,3,) where [x] denotes the integral part of x. The present note generalizes this result to the case of the pair of sequences {[f(k)]}, {[g(k)]} with suitable hypotheses on the functions f and g. The special case f(x)=αx, g(x)=βx is the result due to Beatty.

Copyright © 1978 Hindawi Publishing Corporation. 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.


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