International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 846161 | https://doi.org/10.1155/S0161171286001011

Curtis N. Cooper, Robert E. Kennedy, "A generalization of a theorem by Cheo and Yien concerning digital sums", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 846161, 4 pages, 1986. https://doi.org/10.1155/S0161171286001011

A generalization of a theorem by Cheo and Yien concerning digital sums

Received20 Jan 1986

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,,(x1)}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,,(x1)}is also (4.5)xlogx+0(x). The constant implicit in the big-oh notation is dependent on k.

Copyright © 1986 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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