Irregular sets of integers generated by the greedy algorithm
Author:
Joseph L. Gerver
Journal:
Math. Comp. 40 (1983), 667676
MSC:
Primary 10L20; Secondary 10H20
MathSciNet review:
689480
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Abstract 
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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. 261264.
 [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 0439796
(55 #12678), http://dx.doi.org/10.1090/S00029939197704397969
 [3]
Joseph
L. Gerver and L.
Thomas Ramsey, Sets of integers with nonlong
arithmetic progressions generated by the greedy algorithm, Math. Comp. 33 (1979), no. 148, 1353–1359. MR 537982
(80k:10053), http://dx.doi.org/10.1090/S00255718197905379820
 [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A. M. Odlyzko & R. P. Stanley, "Some curious sequences constructed with the greedy algorithm," unpublished Bell Laboratories report, January 1978.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 (1960/1961), 332–344 (1960/61). MR 0142526
(26 #95)
 [1]
 P. Erdös & P. Turan, "On certain sequences of integers," J. London Math. Soc., v. 11, 1936, pp. 261264.
 [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. 211214. 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. 13531359. 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 A. M. Odlyzko & R. P. Stanley, "Some curious sequences constructed with the greedy algorithm," unpublished Bell Laboratories report, January 1978.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. 332344. MR 0142526 (26:95)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198306894802
PII:
S 00255718(1983)06894802
Article copyright:
© Copyright 1983
American Mathematical Society
