On the Change Rule of 3<i>x</i> + 1 Problem

Abstract

This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number; 2) The odd number must change to a number of LiKe’s second sequence {3n – 1| n ∈ Z+}; 3) Then this 3n - 1 will change to a smaller 3n – 1 and gradually decrease to 8 (that is 32 - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2n (it might even explain 2n). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.