Geometric progressions in syndetic sets

Patil, Bhuwanesh Rao

doi:10.1007/s00013-019-01320-x

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2019

2023

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Cited by 5 publications

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“…He [11] shows by a computer search that any subset of the range [1,640] containing at least one of any pair of consecutive numbers must contain three term geometric progressions. Recently Patil [17] shows that any sequence of integers s 1 < s 2 < · · · with s n − s n−1 ≤ 2 must contain infinitely pairs {a, ar 2 } with r an integer.…”

Section: Introductionmentioning

confidence: 99%

Primitive and geometric-progression-free sets without large gaps

McNew

2020

Acta Arith.

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We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of prime numbers. The proof uses the probabilistic method. Using the same techniques we improve the bounds obtained by He for gaps in geometric-progression-free sets.2010 Mathematics Subject Classification. 11N25 (primary), and 11B05 (secondary).

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Section: Introductionmentioning

confidence: 99%