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A057215
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[1->01, 2->10, 3->01]-transform of 3-symbol Thue-Morse A026600.
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3
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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
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OFFSET
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0,1
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COMMENTS
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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.
(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)
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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