On sequences without geometric progressions

Brown, Brienne; Gordon, Daniel

doi:10.1090/S0025-5718-96-00765-X

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.

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