Joe Chung
Monmouth U. Homepage

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====== Ulam Sequence ======

Write and save a program //Ulam.java//.

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

<code>
          • 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.
</code>

Here are some sequences for the starting integers 2-7:

<code>
          2 ->  1
          3 -> 10 ->  5 -> 16 ->  8 ->  4 ->  2 ->  1
          4 ->  2 ->  1
          5 -> 16 ->  8 ->  4 ->  2 ->  1
          6 ->  3 -> <repeat Ulam sequence for 3>
          7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13
            -> 40 -> 20 -> 10 -> 5 -> <repeat Ulam sequence for 5>
</code>

Write //Ulam.java// so that it inputs a number from the user and prints the Ulam sequence for it, using a //while// loop. Here are some example user dialogs:

<code>
          Enter a positive integer to show its Ulam sequence:
          2
          The Ulam sequence is:
          2 -> 1




          Enter a positive integer to show its Ulam sequence:
          3
          The Ulam sequence is:
          3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
</code>

Here is an algorithm for this program:

<code>
          Read n
          
          Compute and print the Ulam sequence for n:
          
          While n is greater than 1
              Print 'n ->'
              If n is even
                 n = n/2
              Else // n is odd
                 n = n*3 + 1
          End While

          Print n // Final value of n is 1
</code>