Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix.

Terms

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