Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); take limit; note positions of 2's.

Terms

a(0) =2a(1) =3a(2) =6a(3) =8a(4) =9a(5) =11a(6) =14a(7) =15a(8) =18a(9) =19a(10) =22a(11) =24a(12) =25a(13) =28a(14) =30a(15) =31a(16) =33a(17) =36a(18) =38a(19) =39a(20) =41a(21) =44a(22) =45a(23) =48a(24) =49a(25) =51a(26) =54a(27) =55a(28) =58a(29) =59