A036586 -id:A036586 - cp's OEIS frontend

A036578 Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2

Offset: 0

N. J. A. Sloane

nonn

Trajectory of 1 under the morphism 0 -> 12, 1 -> 102 & 2 -> 0. - Robert G. Wilson v, Apr 06 2008

Brian Hayes, Group Theory in the Bedroom and other Mathematical Diversions, Hill and Wang, A division of Farrar, Straus and Giroux, NY, 2008, pages 190-194.
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 26.

Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (1) (2012) 42-46.
Index entries for sequences that are fixed points of mappings

Cf. A005679, A036577, A036579, A036580, A036581, A036582, A036583, A036584, A036585, A036586.

Nest[ # /. {0 -> {1, 2}, 1 -> {1, 0, 2}, 2 -> {0}} &, {0}, 7] // Flatten (* Robert G. Wilson v, Apr 06 2008 *)

A234538 (Number of positive digits of n written in base 3) modulo 3.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1

Offset: 0

Vladimir Shevelev, Jan 13 2014

Since A000120 is the number of positive digits of n written in binary, this sequence is a formal ternary analog of the Thue-Morse sequence A010060. However, one cannot name it a "ternary version of A010060" like the known versions A053838, A071858, A036577-A036586, since it is not "cubefree"; i.e., it contains the same 3 consecutive terms, and there is not a known morphism for which it is a fixed point.

Peter J. C. Moses, Table of n, a(n) for n = 0..999

Cf. A000120, A010060, A036577-A036586, A053838, A071858, A160384.

a[n_] := Mod[Plus @@ DigitCount[n, 3, {1, 2}], 3]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

a(n)=my(d=digits(n, 3)); sum(i=1, #d, !d[i])%3 \\ Charles R Greathouse IV, Jan 13 2014

A160384(n) == a(n) (mod 3).

cp's OEIS Frontend

A036578 Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

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