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

Article copyright:
© Copyright 1984
American Mathematical Society