文章基本信息

标题：Collatz Sequences and Characteristic Zero-One Strings: Progress on the 3<i>x</i> + 1 Problem
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作者：David C. Kay
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2021
卷号：11
期号：3
页码：226-239
DOI：10.4236/ajcm.2021.113015
语种：English
出版社：Scientific Research Publishing
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.
关键词：Generator;Resultant;3x+ 1 Cycle