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Averaging the sum of digits function to an even base

Published online by Cambridge University Press:  20 January 2009

D. M. E. Foster
D. M. E. Foster
Affiliation:
Mathematical InstituteUniversity of St AndrewsNorth HaughSt Andrews KY16 9SS
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Abstract

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For a fixed integer q≧2, every positive integer where each ar(q, k) ∈ {0, 1, 2, …, q–1}. The sum of digits function α(q, k) = behaves rather erratically but on averaging has a uniform behaviour. In particular if A(q, n) = , where n > 1, then it is well known that A(q, n)∼½ ((q – 1)/log q) n log n as n→∞. For even values of q, a lower bound is now given for the difference ½S(q, n) = A(q, n)–½(q–1)[logn/logq] n, where [log n/log q] denotes the greatest integer ≦ log n/log q, complementing an earlier result for odd values of q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 449 - 455
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

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