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 | References | Similar Articles | Additional Information

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]**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**439796**, https://doi.org/10.1090/S0002-9939-1977-0439796-9**[3]**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**[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M. Odlyzko & R. P. Stanley, "Some curious sequences constructed with the greedy algorithm," unpublished Bell Laboratories report, January 1978.**[5]**A. M. Odlyzko, private communication.**[6]**R. A. Rankin,*Sets of integers containing not more than a given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**65**(1960/61), 332–344 (1960/61). MR**142526**

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

Article copyright:
© Copyright 1983
American Mathematical Society