Density Bounds for the 3x + 1 Problem. II. Krasikov Inequalities

David Applegate, Jeffrey C. Lagarias
1995 Mathematics of Computation  
Dedicated to the memory of D. H. Lehmer) for some constant γ > 0. In part I we showed one can take γ = .643 using an approach started by Crandall [2] and extended by Sander [5]. In this paper we derive bounds (1.3) using systems of difference inequalities found by Krasikov [3]. For each k ≥ 2 there is a system ( k of such inequalities; Krasikov [3] used ( 2 to
doi:10.2307/2153346 fatcat:piebn4g3u5fwjimdrgmtbvwaji