A057215 [1->01, 2->10, 3->01]-transform of 3-symbol Thue-Morse A026600.

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

Offset: 0

Author

Richard Blavy, Sep 24 2000

Keywords

• nonn

Comments

Old name was: Analog of A026600 using instead of 1: 0,1; instead of 2: 1,0; instead of 3: 0,1.

A nonperiodic sequence of 0 and 1, with one 0 and one 1 in every subsequence of three terms.

From Michel Dekking, Apr 17 2019: (Start):

(a(n)) is a morphic sequence, i.e., a letter-to-letter projection of a fixed point of a morphism.

Let the morphism sigma be given by

1->123, 2->456, 3->345, 4->612, 5->561, 6->234,

and let the letter-to-letter map delta be given by

1->0, 2->1, 3->1, 4->0, 5->0, 6->1.

Then (a(n)) = delta(x), with x the fixed point of sigma starting with 1.

This representation can be obtained by doubling 1,2 and 3, and renaming the resulting six letters as 1,2,3,4,5,6.

(End)

This sequence essentially equals A026605, which is its standard form: a(n) = A026605(n)-1 for all n. - Michel Dekking, Apr 18 2019

Links

• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A026600, A026605

Programs

Mathematica

Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 3}, 2 -> {2, 3, 1}, 3 -> {3, 1, 2}}] &, {1}, 4] /. {1 -> {0, 1}, 2 -> {1, 0}, 3 -> {0, 1}}] (* Robert G. Wilson v, Mar 09 2005 *)

Extensions

Name changed by Michel Dekking, Apr 17 2019