International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 817-820
doi:10.1155/S0161171286001011
A generalization of a theorem by Cheo and Yien concerning digital sums
Department of Mathematics and Computer Science, Central Missouri State University, Warrensburg 64093, Missouri, USA
Received 20 January 1986
Copyright © 1986 Curtis N. Cooper and Robert E. Kennedy. 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.
Abstract
For a non-negative integer n, let s(n) denote the digital sum of n. Cheo and Yien proved that for a positive integer x, the sum of the terms of the sequence{s(n):n=0,1,2,…,(x−1)}is (4.5)xlogx+0(x). In this paper we let k be a positive integer and determine that the sum of the sequence{s(kn):n=0,1,2,…,(x−1)}is also (4.5)xlogx+0(x). The constant implicit in the big-oh notation is dependent on k.