Iteration Steps of 3x+1 Problem

On the 3x+1 problem, given a positive integer $N$, let $D\left(N\right)$, $O\left(N\right)$, $E\left(N\right)$ be the total iteration steps, the odd iteration steps and the even iteration steps when $N$ iterates to 1(except 1) respectively. Trivially, we have $D\left(N\right)=O\left(N\right)+E\left(N\right)$. In this paper, we propose a so-called weak residue conjecture(i.e., $\frac{2^{E\left(N\right)}}{3^{O\left(N\right)}\cdot N}\le 2$). We prove that if 3x+1 conjecture is true and the weak residue conjecture is true, there exist non-trivial relationships among $D\left(N\right)$, $O\left(N\right)$, $E\left(N\right)$, i.e., $O\left(N\right)=\lfloor {\log }_{6}2\cdot D\left(N\right)-{\log }_{6}N\rfloor$(it implies that we can calculate $O\left(N\right)$, $E\left(N\right)$ directly by $D\left(N\right)$ only, of course given $N$), and 5 more similar equations are derived simultaneously.