The following question goes by several names, the Collatz Algorithm, the Syracuse Problem, or sometimes just the 3n+1-problem,and it is simply the observation that, observation that, beginning any number n, the following process always seems to end with the number 1.
If n is even divide it by 2, while if n is odd, replace it by 3n+1.
For example, beginning with n = 7 we are led by rules through the following sequence: