Collatz Sequences and Characteristic Zero-One Strings: Progress on the 3<i>x</i>+ 1 Problem
Collatz Sequences and Characteristic Zero-One Strings: Progress on the 3<i>x</i>+ 1 Problem作者机构:Asheville USA
出 版 物:《American Journal of Computational Mathematics》 (美国计算数学期刊(英文))
年 卷 期:2021年第11卷第3期
页 面:226-239页
学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题:Generator Resultant 3x + 1 Cycle
摘 要:The unsolved number theory problem known as the 3x + 1 problem involves sequences of positive integers generated more or less at random that seem to always converge to 1. Here the connection between the first integer (n) and the last (m) of a 3x + 1 sequence is analyzed by means of characteristic zero-one strings. This method is used to achieve some progress on the 3x + 1 problem. In particular, the long-standing conjecture that nontrivial cycles do not exist is virtually proved using probability theory.