A071762 Leftmost 1 is converted to a 2, which then propagates one step at a time until it is rightmost; then it changes to a pair of 1's and the process repeats.

0, 1, 2, 11, 21, 12, 111, 211, 121, 112, 1111, 2111, 1211, 1121, 1112, 11111, 21111, 12111, 11211, 11121, 11112, 111111, 211111, 121111, 112111, 111211, 111121, 111112, 1111111, 2111111, 1211111, 1121111, 1112111, 1111211, 1111121, 1111112