On sequences without geometric progressions
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- by Brienne E. Brown and Daniel M. Gordon PDF
- Math. Comp. 65 (1996), 1749-1754 Request permission
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.References
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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
- MR Author ID: 75440
- Email: gordon@ccrwest.org
- Published electronically: October 1, 1996
- Journal: Math. Comp. 65 (1996), 1749-1754
- MSC (1991): Primary 11B05; Secondary 11B83
- DOI: https://doi.org/10.1090/S0025-5718-96-00765-X
- MathSciNet review: 1361804