A generalization of a theorem by Cheo and Yien concerning digital sums
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,...
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| Format: | Article |
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Hindawi Limited
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286001011 |
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doaj-967b43a49dba4b779ff6cb688a4eb7f72020-11-25T00:32:17ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019481782010.1155/S0161171286001011A generalization of a theorem by Cheo and Yien concerning digital sumsCurtis N. Cooper0Robert E. Kennedy1Department of Mathematics and Computer Science, Central Missouri State University, Warrensburg 64093, Missouri, USADepartment of Mathematics and Computer Science, Central Missouri State University, Warrensburg 64093, Missouri, USAFor 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.http://dx.doi.org/10.1155/S0161171286001011digital sums. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Curtis N. Cooper Robert E. Kennedy |
| spellingShingle |
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 digital sums. |
| author_facet |
Curtis N. Cooper Robert E. Kennedy |
| author_sort |
Curtis N. Cooper |
| title |
A generalization of a theorem by Cheo and Yien concerning digital sums |
| title_short |
A generalization of a theorem by Cheo and Yien concerning digital sums |
| title_full |
A generalization of a theorem by Cheo and Yien concerning digital sums |
| title_fullStr |
A generalization of a theorem by Cheo and Yien concerning digital sums |
| title_full_unstemmed |
A generalization of a theorem by Cheo and Yien concerning digital sums |
| title_sort |
generalization of a theorem by cheo and yien concerning digital sums |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1986-01-01 |
| description |
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. |
| topic |
digital sums. |
| url |
http://dx.doi.org/10.1155/S0161171286001011 |
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