On sequences without geometric progressions

Authors:
Brienne E. Brown and Daniel M. Gordon

Journal:
Math. Comp. **65** (1996), 1749-1754

MSC (1991):
Primary 11B05; Secondary 11B83

Published electronically:
October 1, 1996

MathSciNet review:
1361804

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Abstract | References | Similar Articles | Additional Information

Abstract: Several papers have investigated sequences which have no -term arithmetic progressions, finding bounds on their density and looking at sequences generated by greedy algorithms. Rankin in 1960 suggested looking at sequences without -term geometric progressions, and constructed such sequences for each 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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Additional Information

**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:
http://dx.doi.org/10.1090/S0025-5718-96-00765-X

Published electronically:
October 1, 1996