A squarefree (or Thue-Morse) ternary sequence: closed under 1->123, 2->13, 3->2. Start with 1.

Terms

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