The sum of the reciprocals of a set of integers with no arithmetic progression of terms

Author:
Joseph L. Gerver

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

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for each integer , there exists a set of positive integers containing no arithmetic progression of *k* terms, such that , with a finite number of exceptional *k* for each real . This result is shown to be superior to that attainable with other sets in the literature, in particular Rankin's sets , which have the highest known asymptotic density for sets of positive integers containing no arithmetic progression of *k* terms.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0439796-9

Keywords:
Arithmetic progression,
sum of reciprocals,
asymptotic density,
Szemerédi's theorem,
Rankin's sets

Article copyright:
© Copyright 1977
American Mathematical Society