The Sally sequence: the length of repetition avoided in A006345.

Terms

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