A005679 A squarefree (or Thue-Morse) ternary sequence: closed under a->abc, b->ac, c->b. (Formerly M0140)

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

1,1

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

Table of n, a(n) for n=1..105.

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

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 *)

Crossrefs

Cf. A005681.

Sequence in context: A048233 A287730 A260452 * A232927 A350651 A275832

Adjacent sequences: A005676 A005677 A005678 * A005680 A005681 A005682

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved