Divergent trajectory. . The Conjecture asserts that all trajectories of positive n are convergent. Call the least positive k for which the stopping time of n , and set if no k occurs with . Also call the least positive k for which the total stopping time of n , and set if no such k occurs. We may restate the Conjecture in terms of the stopping time as follows.
Every integer has a finite stopping time .
The appeal of the problem lies in the irregular behavior of the successive iterates . One can measure this behavior using the stopping time, the total stopping time, and the expansion factor defined by if n has a bounded trajectory and if n has a divergent trajectory. Behavior of iterates . The Conjecture has been numerically checked for a large range of values of n . It is an interesting problem to find efficient algorithms to test the conjecture on a computer.