# C++: Programming Problem - Ulam Sequence

## The Ulam Sequence

A mathematician named Ulam proposed generating a sequence of numbers from any positive integer n (n > 0) as follows:

- If n is 1, stop.
- If n is even, the next number is n/2.
- If n is odd, the next number is 3*n + 1.
- Continue with this process until reaching 1.

Here are some examples for the first few integers.

       2 ->  1
       3 -> 10 ->  5 -> 16 ->  8 ->  4 ->  2 ->  1
       4 ->  2 ->  1
       5 -> 16 ->  8 ->  4 ->  2 ->  1
       6 ->  3 -> etc as for 3 above.
       7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> see 5 above.

## Write a program that shows the sequence

Write a program that reads a number (in a while loop of course) and prints the Ulam sequence for it.