Necklace Problem Help

Hey guys, I'm a beginner programmer (so don't assume that I would know anything) and I'm having trouble with this necklace problem. Some of you probably know what it is, but I'll post it anyway:
An interesting problem in number theory is sometimes called the “necklace problem.” This problem begins with two single-digit numbers. The next number is obtained by adding the first two numbers together and saving only the ones-digit. This process is repeated until the “necklace” closes by returning to the original two numbers. For example, if the starting numbers are 1 and 8, the output would look like:
18976392134718
Can anyone post the basic code for this, because I am just getting into iteration and this is all sort of confusing for me. I know what to do to solve the problem mathematically, but the variables are really tricky because you have to assign new values to existing variables. Also, I'm pretty sure a do-while loop will work here, but I do not know the specifics. Please, any help would be greatly appreciated.

Ok, sorry about that.
What I have is:
public class Necklace
     public static void main(String[] args)
          String output = "";
          String first, second;
          first = JOptionPane.showInputDialog ("Enter a single-digit number:");
          second = JOptionPane.showInputDialog ("Enter another single-digit number:");
          int f = Integer.parseInt (first);
          int s = Integer.parseInt (second);
          int sum = f + s;
          int next = sum%10;
          int previous = s;
          while (previous != f && next !=s)
               sum = next + previous;
               previous = next;
               next = sum%10;
               output += (next + "");
               JOptionPane.showMessageDialog (null, output, "Necklace", JOptionPane.PLAIN_MESSAGE);
I'm not sure where I'm off, but when I run it the output begins with 7 (the fourth term in the sequence) and ends with a 3 (the 10th term). I do not know how to get it to begin with the original two values that the user inputs, because those variables change, and I am not sure why it is not continuing to the end. Also, this is fairly minor, but is there a way to get the entire sequence to appear in one pop-up message dialog box, instead of the sequence gaining one value at a time after clicking OK? Thanks in advanced.

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    Message was edited by: md monirujjaman
    Message was edited by: md monirujjaman

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