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The density of subsequences

Published online by Cambridge University Press:  17 April 2009

David B. Choate
David B. Choate
Affiliation:
Department of Mathematics, Xavier University of Louisian, New Orleans, Louisiana 70125, USA.
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Let A = {a1, a2, …} be an increasing sequence of positive integers whose upper density, θ, is less than 1, Then the counting function of the subsequence does not exceed .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 2 , April 1984 , pp. 145 - 149
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Mann, Henry B., Addition theorems: the addition theorems of group theory and number theory (Interscience [John Wiley & Sons], New York, London, Sydney, 1965).Google Scholar
[2]Niven, Ivan and Zuckerman, Herbert S., An introduction to the theory of numbers, Second edition (John Wiley & Sons, New York, London, Sydney, 1966).Google Scholar