A308901 Lexicographically earliest overlap-free binary sequence.

0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1

Offset

1

Comments

Complement of A080813.

References

M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 20 (definition of "overlap").

J. Shallit, A second course in formal languages and automata theory, Cambridge, 2009, pp. 37-39.

Links

Table of n, a(n) for n=1..108.

J.-P. Allouche, J. Currie, and J. Shallit, Extremal infinite overlap-free binary words, Elect. J. Combin., 5:1 (1998), #R27.

J.-P. Allouche and Jeffrey Shallit, The Ubiquitous Prouhet-Thue-Morse Sequence, in C. Ding. T. Helleseth and H. Niederreiter, eds., Sequences and Their Applications: Proceedings of SETA '98, Springer-Verlag, 1999, pp. 1-16.

Formula

0,0,1,0,0,1 followed by a version of the Thue-Morse sequence A010060.

Mathematica

Join[{0, 0, 1, 0, 0, 1}, 1-ThueMorse[Range[0, 200]]] (* Paolo Xausa, Dec 19 2023 *)

Crossrefs

Cf. A010060, A080813, A282317 (cubefree analog).

Sequence in context: A288213 A308187 A289007 * A286804 A188071 A343219

Adjacent sequences: A308898 A308899 A308900 * A308902 A308903 A308904

Keyword

nonn

Author

N. J. A. Sloane, Jul 16 2019

Status

approved