Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2), take limit.

Terms

a(0) =1a(1) =2a(2) =2a(3) =1a(4) =1a(5) =2a(6) =1a(7) =2a(8) =2a(9) =1a(10) =2a(11) =1a(12) =1a(13) =2a(14) =2a(15) =1a(16) =1a(17) =2a(18) =2a(19) =1a(20) =1a(21) =2a(22) =1a(23) =2a(24) =2a(25) =1a(26) =1a(27) =2a(28) =1a(29) =2