摘要
给定一个大于1的正整数n,它的下一个数由n的奇偶性决定。如果n是偶数,则下一个数为n/2,否则为3n+1。重复这样的运算,直到得到1为止。科拉茨(Collatz)猜想:对于任意给定的正整数n,经过有限步后,一定可以得到1。本文给出一个Collatz序列的Collatz-Binary算法,将Collatz序列的计算简化到只计算奇数情形,引入一个新的停时概念,并研究Collatz序列相关性质,给有限终止分析提供一种新的途径。
Given a number n, its next number is decided by the parity of n. If n is even, then the number is n~ 2, otherwise 3n ＋ 1. One repeats the above procedure until getting 1. The resulting sequence generated by this method is called the Collatz sequence of n. Collatz conjecture is ： given an arbitrary positive integer n, it will stop in 1 after a finite of steps. The paper gives an algorithm, Collatz-Binary, which is based on calculus of binary string, reducing the calculation of Collatz sequence to only consider the odd number. We introduce a new stop- ping time and investigate related property of Collatz sequence. The Collatz-Binary algorithm reduces the Collatz sequence, bringing convenience to finite termination analysis.
出处
《贵州大学学报（自然科学版）》
2015年第5期60-65,共6页
Journal of Guizhou University:Natural Sciences
基金
国家自然科学基金项目资助(61262006)
关键词
Collatz猜想
3n+1问题
串算法
停时
Collatz conjecture
3n ＋ 1 problem
calculus of binary string
stopping time
