3X+1迭代数列的几个性质  

Several Properties of 3X+1 Iterative Sequences

作　　者：吴拿达 WU Na-da(College of Mathematics and Statistics,Hanshan Normal University,Chaozhou,Guangdong,521041)

机构地区：[1]韩山师范学院数学与统计学院,广东潮州521041

出　　处：《韩山师范学院学报》2022年第3期1-4,共4页Journal of Hanshan Normal University

摘　　要：3X+1迭代数列与Collatz猜想密切相关,对其进行研究有助于揭开Collatz猜想的面纱.在本文中,3X+1迭代数列的若干性质将被给出并加以证明,包括用一类常系数线性非齐次递推关系的求解来证明其不具有严格单调性,又利用同余的知识证明其除了首项外其余各项皆不能被3整除的性质.最后对其3X+1迭代数列从第二项开始恒等于1的正奇数进行刻画,给出表达式.3X+1 iterative sequences are closely related to the Collatz conjecture,and research on them is helpful to uncover the veil of the Collatz conjecture.In this paper,several properties of 3X+1 iterative sequences are presented and proved,including proving that it is not strictly monotonic by seeking the solution of a kind of linear and non-homogeneous recurrence relation with constant coefficients,and proving the property that all terms except the first term of every 3X+1 iterative sequence are not divisible by 3 by using the knowledge of congruence.And finally,the expression is given for the positive odd numbers of the corresponding 3X+1 iterative sequences,which are constantly equal to 1 from the second term onwards.

关 键 词：Collatz猜想 3X+1迭代数列 单调性 回归于1的数 递推关系 

分 类 号：O156[理学—数学]