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

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.