自然数数码和的m次方映射数列的周期性

The Cyclicity Reflected on M Power's Addition of Natural Numbers

证明了自然数数码和的m次方映射数列{nk}为周期数列,给出了当m=2,3,4,5,6时,{nk}的周期节及对任意自然数n,必存在自然数k0,当k≥k0时,Tk(n)进入相应周期节的条件。

This paper has found that m power's addition of natural numbers {nk} is cyclicity. Given m=2,3,4, 5,6; {nk} Circular knot to arbitrary numbers is sure to have a natural number k0, when k≥ k0, Tk(n) will enter into its relevant Circular knot .