Irregular sets of integers generated by the greedy algorithm

Author:
Joseph L. Gerver

Journal:
Math. Comp. **40** (1983), 667-676

MSC:
Primary 10L20; Secondary 10H20

DOI:
https://doi.org/10.1090/S0025-5718-1983-0689480-2

MathSciNet review:
689480

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Abstract: The greedy algorithm was used to generate sets of positive integers containing no subset of the form , , , , , and , respectively. All of these sets have peaks of density in roughly geometric progression.

**[1]**P. Erdös & P. Turan, "On certain sequences of integers,"*J. London Math. Soc.*, v. 11, 1936, pp. 261-264.**[2]**J. L. 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)****[3]**J. L. Gerver & L. T. Ramsey, "Sets of integers with no long arithmetic progressions generated by the greedy algorithm,"*Math. Comp.*, v. 33, 1979, pp. 1353-1359. MR**537982 (80k:10053)****[4]**A. M. Odlyzko & R. P. Stanley, "Some curious sequences constructed with the greedy algorithm," unpublished Bell Laboratories report, January 1978.**[5]**A. M. Odlyzko, private communication.**[6]**R. A. Rankin, "Sets of integers containing not more than a given number of terms in arithmetical progression,"*Proc. Roy. Soc. Edinburgh Sect.*A, v. 65, 1960/1961, pp. 332-344. MR**0142526 (26:95)**

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0689480-2

Article copyright:
© Copyright 1983
American Mathematical Society