Lower bounds for the total stopping time of 3X+1 iterates
| dc.creator | Applegate, David | |
| dc.creator | Lagarias, Jeffrey C. | |
| dc.date | 2001-03-08 | |
| dc.date.accessioned | 2026-07-07T04:40:33Z | |
| dc.date.available | 2026-07-07T04:40:33Z | |
| dc.description | The 3X+1 function T(n) is (3n+1)/2 if n is odd and n/2 if n is even. The total stopping time σ_\infty (n) for a positive integer n is the number of iterations of the 3x+1 function to reach 1 starting from n, and is \infty if 1 is never reached. The 3x+1 conjecture states that this function is finite. We show that infinitely many n have a finite total stopping time with σ_\infty(n) > 6.14316 log n. The proof uses a very large computation. It is believed that almost all positive integers have σ_\infty (n) > 6.95212 \log n. The method of the paper should extend to prove infinitely many integers have this property, but it would require a much larger computation. | |
| dc.description | 21 pages latex, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0103054 | |
| dc.identifier | http://arxiv.org/abs/math/0103054 | |
| dc.identifier | Math. Comp. 72 (2003), 1035--1049. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61062 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.subject | 11B83; 11Y16 | |
| dc.title | Lower bounds for the total stopping time of 3X+1 iterates | |
| dc.type | text |