0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2...

Starting at the left, as you add terms, when and how big is the largest proportion of each number? For example 3 of the first 5 terms are 1s.

Show that as the sequence is continued indefinitely, no number appears with a proportion greater than 0.