Trajectory of 1 under the morphism 1 -> 12, 2 -> 123, 3 -> 1234, etc.

Terms

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