次数k≤10的Steinhaus循环的计算

COMPUTATION OF STEINHAUS CYCLES FOR POWER k≤10

本文综合运用数学与程序设计的方法,给出了次数k≤10的全部Steinhaus循环,其中k=5的结论更正了现有文献中的疏漏,6≤k≤10的结论是新的。

Let k be a fix positive integer. For any natural number calculates Then for the integer β_1, calclates the sum of k-powers of all digits a_i of β_1, and repeats this process for β_i. All cyclic parts for power k≤10 are decided with the computer, and also an omision for k=5 in the paper of K. Iseki et al. is pointed out.