3N+1猜想中周期数的研究

Study of periodic numbers in 3N+1 conjecture

给出了关于 3N +1猜想中周期数存在的一个必要条件 :Sl(mxi) =nxi,并在此基础上推广为Sl(σbxi)=nb + 1xi.且给出周期数x1的具体表达式x1=r1/(1- 3l/2 k) .证明了圈长为 2和

A necessary condition about the existence of periodic numbers in 3N+1 conjecture: S^l(mx_i)=nx_i, and its generalized necessary condition: S^l(σ_bx_i)=n^(b+1)x_i were presented. A formula about periodic numbers was given, where x_1=r_1/(1-3~l/2~k). It was proved that the length of periodic numbers being 2 or 3 could not exist.