关于Collatz猜想的发现（英文）

Discoveries on Collatz conjecture

提出了3n+1问题的两个新观点.一个观点是关于数位移动的问题,揭示了3n+1问题以及相关的推广问题中的运算与相应数字系统中数字串的移动是等价的.另一个观点是关于3n+1问题中的数论函数的一个特殊假设图的存在问题.文章呈现了这个猜想以及相关推广中的一些新的发现.它们包括经典的3n+1问题中绝大部分数字通过数字5进入最终循环的现象,以及在3进制数字系统中绝大部分数字进入一个特殊循环的现象.

The paper provides two new points of view at the problem of 3n+1.One is a place shift problem demonstrating that the operations involved in the problem of 3n+1 and its generalizations are equivalent to shifting sequences of digits expressed in a number system with a proper base.The other one is a problem about the existence of a particular hypothetical graph for the number theoretical function of the problem of 3n+1.Some new discoveries about the problem and its generalizations are presented in the paper.These include the phenomenon that the majority of the numbers entering the final cycle through the number 5 on the classical problem of 3n+1 and the phenomenon that the majority of the numbers entering a specific cycle on a generalized problem in the number system with base 3.