Regular Section
On the Glide of the 3x+1 Problem
2019 Volume E102.A Issue 3 Pages 613-615
Details
2019 Volume E102.A Issue 3 Pages 613-615
For any positive integer n, define an iterated function $f(n)=\left\{ \begin{array}{ll} n/2, & \mbox{ $n$ even, } 3n+1, & \mbox{ $n$ odd. } \end{array} \right.$ Suppose k (if it exists) is the lowest number such that fk(n)<n, and the operation of “multiplying by 3 and adding one” occurs O(n) times and that of “dividing by 2” occurs E(n) times from n to fk(n). We conjecture that 2E(n)-1<3O(n)<2E(n). This conjecture is similar to the conjecture proposed by Terras in 1976, and we also give an upper bound for the residual term of n.
