A005679 A squarefree (or Thue-Morse) ternary sequence: closed under a->abc, b->ac, c->b.

2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Fixed point of the morphism 1 -> 23, 2 -> 213 & 3 -> 1. - Robert G. Wilson v, Apr 06 2008

Replacing all 4's in A005681 with 1's yields this sequence. - Sean A. Irvine, Aug 04 2016

References

• A. Salomaa, Jewels of Formal Language Theory. Computer Science Press, Rockville, MD, 1981, p. 10.
• G. Siebert, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Marston Morse and Gustav A. Hedlund, Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J., Volume 11, Number 1 (1944), 1-7.
• G. Siebert, Letter to N. J. A. Sloane, Sept. 1977.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A005681.

Programs

Mathematica

Nest[ # /. {1 -> {2, 3}, 2 -> {2, 1, 3}, 3 -> 1} &, {2}, 7] // Flatten (* Robert G. Wilson v, Apr 06 2008 *)
SubstitutionSystem[{1->{2,3},2->{2,1,3},3->{1}},{2},{7}][[1]] (* Harvey P. Dale, Jul 14 2022 *)

Extensions

More terms from Robert G. Wilson v, Apr 06 2008