A057215 - OEIS

%I #22 Apr 18 2019 04:50:34

%S 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,

%T 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,

%U 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

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

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

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

%C From _Michel Dekking_, Apr 17 2019: (Start):

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

%C Let the morphism sigma be given by

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

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

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

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

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

%C (End)

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

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%t 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 *)

%Y Cf. A026600, A026605

%K nonn

%O 0,1

%A _Richard Blavy_, Sep 24 2000

%E Name changed by _Michel Dekking_, Apr 17 2019