A nonaveraging set of integers with a large sum of reciprocals

Author:
J. Wróblewski

Journal:
Math. Comp. **43** (1984), 261-262

MSC:
Primary 11B25

DOI:
https://doi.org/10.1090/S0025-5718-1984-0744935-8

MathSciNet review:
744935

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Abstract: A set of integers is constructed with no three elements in arithmetic progression and with a rather large sum of reciprocals.

**[1]**F. A. Behrend,*On sets of integers which contain no three terms in arithmetical progression*, Proc. Nat. Acad. Sci. U. S. A.**32**(1946), 331–332. MR**0018694****[2]**Paul Erdős,*Problems and results in combinatorial number theory*, Journees Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, Bordeaux, 1974), Soc. Math. France, Paris, 1975, pp. 295–310. Astérisque, Nos. 24-25. MR**0374075****[3]**P. Erdös & P. Turan, "On some sequences of integers,"*J. London Math. Soc.*, v. 11, 1936, pp. 261-264.**[4]**Joseph L. Gerver,*The sum of the reciprocals of a set of integers with no arithmetic progression of 𝑘 terms*, Proc. Amer. Math. Soc.**62**(1977), no. 2, 211–214. MR**0439796**, https://doi.org/10.1090/S0002-9939-1977-0439796-9**[5]**Joseph L. Gerver and L. Thomas Ramsey,*Sets of integers with no long arithmetic progressions generated by the greedy algorithm*, Math. Comp.**33**(1979), no. 148, 1353–1359. MR**537982**, https://doi.org/10.1090/S0025-5718-1979-0537982-0

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0744935-8

Article copyright:
© Copyright 1984
American Mathematical Society