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

Terms

a(0) =1a(1) =4a(2) =5a(3) =7a(4) =10a(5) =12a(6) =13a(7) =16a(8) =17a(9) =20a(10) =21a(11) =23a(12) =26a(13) =27a(14) =29a(15) =32a(16) =34a(17) =35a(18) =37a(19) =40a(20) =42a(21) =43a(22) =46a(23) =47a(24) =50a(25) =52a(26) =53a(27) =56a(28) =57a(29) =60