柯拉兹猜想重访:一个初等推广

Pub Date : 2020-07-01 DOI:10.2478/ausm-2020-0007

Amauri Gutiérrez

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引用次数: 2

摘要

摘要:Collatz猜想指出，对偶数自然数n到n2 {n \ / 2}和奇数自然数n到3n + 1的映射进行迭代，最终得到1。本文分析了Collatz猜想的一种新的推广，得到了一些有趣的结果。由于Collatz猜想可以看作是本文所介绍的泛化的一个特例，所以本文还提出了几个更一般的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Collatz conjecture revisited: an elementary generalization

Abstract Collatz conjecture states that iterating the map that takes even natural number n to n2 {n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.

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