Write down a sequence of random (positive, whole) numbers which are not very large (say within a factor of ten or so) compared to its length. Start anywhere not very far from the end of the sequence (say within the first half or so). Walk as many numbers down the line as there are units contained in the number you are currently in. Do this repeatedly until you can no longer do so without extrapolating the sequence. I will then say you are at your final destination. Then, for almost all such sequences and almost all initial positions, the final destination is a constant which depends only on the sequence, but not on the initial position. (In a sense I cannot define precisely but if you do the experiment with concrete numbers, you will see that the probabilities are astoundingly high).
Does anyone know the name of this phenomenon? Does anyone know an explanation for it?
Thank you for your answer(s).