[ShoeNinja]

You could just check the character right after the 1 that you find and make sure it isn't a 1 as well.

Code:

int i = String.indexOf("1");
if( i != -1 && !String.charAt(i).equals("1")){

}

You could also do an indexOf("1") and an indexOf("11") and compare them. If they are the same then you have 11 and not 1.

The problem with these solutions is that they are very specific. I would probably write my own method using the first technique. I would pass it the character to look for and it would return the position only if the character was repeated.