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Mathematics of Computation

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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: 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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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

Published electronically: October 1, 1996