On The Glide Of The 3x+1 Problem

For any positive integer n, define an iterated function f(n) = {n/2, n even, 3n+1, n odd. Suppose k (if it exists) is the lowest number such that f(k)(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 f(k)(n). We conjecture that 2(E(n)-1) < 3(O(n)) < 2(E(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.