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

Curtis N. Cooper and Robert E. Kennedy

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-4

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 ) x log x + 0 ( x ) . In this paper we let k be a positive integer and determine that the sum of the sequence { s ( k n ) : n = 0 , 1 , 2 , … , ( x − 1 ) } is also ( 4.5 ) x log x + 0 ( x ) . The constant implicit in the big-oh notation is dependent on k .

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:846161

DOI: 10.1155/S0161171286001011

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