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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.


References [Enhancements On Off] (What's this?)

  • [1] F. Behrend, "On sets of integers which contain no three terms in an arithmetic progression," Proc. Nat. Atad. Sci. U.S.A., v. 32, 1946, pp. 331-332. MR 0018694 (8:317d)
  • [2] P. Erdös, "Problems and results in combinatorial number theory," Astérisque, v. 24-25, 1975, pp. 295-310. MR 0374075 (51:10275)
  • [3] P. Erdös & P. Turan, "On some sequences of integers," J. London Math. Soc., v. 11, 1936, pp. 261-264.
  • [4] J. Gerver, "The sum of the reciprocals of a set of integers with no arithmetic progression of k terms," Proc. Amer. Math. Soc., v. 62, 1977, pp. 211-214. MR 0439796 (55:12678)
  • [5] J. Gerver & L. Ramsey, "Sets of integers with no long arithmetic progressions generated by the greedy algorithm," Math. Comp., v. 33, 1979, pp. 1353-1360. MR 537982 (80k:10053)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0744935-8
Article copyright: © Copyright 1984 American Mathematical Society

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