Mathematics of Computation

Author(s): Brienne E. Brown; Daniel M. Gordon.
Journal: Math. Comp. 65 (1996), 1749--1754.
MSC (1991): Primary 11B05; Secondary 11B83
Posted: October 1, 1996
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Abstract: Several papers have investigated sequences which have no $k$

-term arithmetic progressions, finding bounds on their density and looking at sequences generated by greedy algorithms. Rankin in 1960 suggested looking at sequences without $k$

-term geometric progressions, and constructed such sequences for each $k$

with positive density. In this paper we improve on Rankin's results, derive upper bounds, and look at sequences generated by a greedy algorithm.

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Brienne E. Brown
Affiliation: 9211 Mintwood Street, Silver Spring, Maryland 20901

Daniel M. Gordon
Affiliation: Center for Communications Research, 4320 Westerra Court San Diego, California 92121
Email: gordon@ccrwest.org

DOI: 10.1090/S0025-5718-96-00765-X
PII: S 0025-5718(96)00765-X
Posted: October 1, 1996

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