Estimate the probability for a number with independently uniformly randomly chosen decimal digits to appear periodic at some point; see https://math.stackexchange.com/questions/2898079.

Question2898079.java

public class Question2898079 {
	public static void main (String [] args) {
		long count = 0;
		long power = 1;
		for (int n = 1;;n++) {
			power *= 10;
			outer:
			for (long k = 0;k < power;k++) {
				String s = String.valueOf (k);
				while (s.length () < n)
					s = '0' + s;
				s += s;
				for (int i = 1;i < n;i++)
					if (s.substring (0,i).equals (s.substring (i,2 * i)))
						continue outer;
				count++;
			}
			System.out.println (n + " : " + count + " : " + count / (double) (power * power));
			count *= 100;
		}
	}
}