You may now the following sequence:
1 11 21 1211 111221 312211 13112221
Explanation of the sequence (I've put an hint just for the ones who want to search a bit ;) )
Where, in each iteration you count the number of occurrence of a digit then put the count and the digit in the new child. (First you've
1, then you've got one
1(11), then you've got two
I've the feeling that the numbers of the sequence will never contains a digit >3 but my mathematics knowledge are way to poor to prove it. So I've made a little program that compute the terms for me to found out if there is a number greater than 3 but up to the 42th term it doesn't find any.
As the length of the string is growing very fast, I can't compute a lot more terms and, even if I was able to do so, this would not be a proof.
So here's the question: How can I prove my feeling?