The sum of the reciprocals of a set of integers with no arithmetic progression of $k$ terms
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- by Joseph L. Gerver PDF
- Proc. Amer. Math. Soc. 62 (1977), 211-214 Request permission
Abstract:
It is shown that for each integer $k \geqslant 3$, there exists a set ${S_k}$ of positive integers containing no arithmetic progression of k terms, such that ${\Sigma _{n \in {S_k}}}1/n > (1 - \varepsilon )k\log k$, with a finite number of exceptional k for each real $\varepsilon > 0$. This result is shown to be superior to that attainable with other sets in the literature, in particular Rankin’s sets $\mathcal {A}(k)$, which have the highest known asymptotic density for sets of positive integers containing no arithmetic progression of k terms.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 211-214
- MSC: Primary 10L10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0439796-9
- MathSciNet review: 0439796