A026606 - OEIS

%I #16 Jul 11 2019 02:08:23

%S 1,2,1,2,2,1,1,2,2,1,1,2,2,1,1,2,1,2,1,2,2,1,1,2,2,1,1,2,1,2,1,2,1,2,

%T 2,1,2,1,1,2,1,2,1,2,1,2,2,1,1,2,2,1,1,2,1,2,2,1,1,2,2,1,1,2,1,2,1,2,

%U 1,2,2,1,2,1,1,2,1,2,1,2,1,2,2,1,1,2,2,1,1,2

%N [1->null]-transform of three-symbol Thue-Morse A026600, with 1 subtracted.

%C Old name was: a(n) = b(n)-1, where b(n) = n-th term of A026600 that is not a 1.

%C From _Michel Dekking_, Apr 18 2019: (Start)

%C This sequence 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

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

%C Then (a(n)) = delta(x), where x = 1234... is a fixed point of sigma.

%C This representation can be obtained by noting that this sequence, with 1 added, can also be viewed as the [1->23, 2->23, 3->32]-transform of A026600, and by doubling 1,2 and 3, renaming the resulting six letters as 1,2,3,4,5,6.

%C (End)

%Y Cf. A026605, A057215.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Name changed by _Michel Dekking_, Apr 18 2019