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A276789
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First differences of A003145.
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5
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4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3, 4, 4, 3, 4, 2, 4, 3, 4, 3, 4, 2, 4, 3
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OFFSET
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1,1
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COMMENTS
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(a(n)) is a fixed point of the tribonacci morphism on the alphabet {4,3,2}, i.e., the morphism given by 4 -> 43, 3 -> 42, 2 -> 4.
To see this, let U := baca, V := baa, W := ba be the three return words of the letter b in the tribonacci word
x = abacabaabacaba... = aUVUW...
[See Justin & Vuillon (2000) for definition of return word. - N. J. A. Sloane, Sep 23 2019]
Under the tribonacci morphism tau given by
tau(a) = ab, tau(b) = ac, tau(c) = a
one obtains
tau(U) = acabaab = b^{-1} UV b,
tau(V) = acabab = b^{-1} UW b,
tau(W) = acab = b^{-1} U b,
which is conjugate to the tribonacci morphism on the alphabet {U,V,W}.
Since these words have lengths 4, 3, and 2, the result follows.
(End)
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LINKS
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FORMULA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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