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A143667
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Digits of the infinite Fibonacci word A003849 grouped 2 by 2 and interpreted as a binary value.
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4
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1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0
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OFFSET
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1,3
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COMMENTS
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Group 2 by 2 the successive letters of the infinite Fibonacci word A003849 then apply: 00->0, 01->1 and 10->2.
Also result of the following iterated morphism: 1->1022, 0->10221, 2->1021, iterated from letter 1. (Monnerot 2008)
Fractal properties studied (proposed for publication)
(a(n)) is essentially the same sequence as A123564. Simply change the alphabet to {1,2,3}, and permute the letters. The Standard Form of (a(n)) written as a word on the alphabet {a,b,c} is abccabccaabc... . Other forms for this standard form are 1,2,3,3,1,2,3,3,1,1,2,3,.... and 123312331123... - _Michel Dekking, Oct 07 2017
(a(n)) is the fixed point of the 2-block map (called 2-block Fibonacci to the power 3) 00->0100101001, 01->01001010, 10->01001001, followed by the coding above. - Michel Dekking, Sep 26 2017
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REFERENCES
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M. Lothaire, Combinatorics on words, Cambridge University Press.
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LINKS
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FORMULA
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a(n) = decimal value of b(2n-1)b(2n), b(n) taken from A003849 (infinite Fibonacci word).
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EXAMPLE
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a(1) = 1 because the infinite Fibonacci word starts with "01", a(2) = 0 because it continues with "00", and so on.
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MATHEMATICA
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Table[3 - (Floor[#1 #2] - 2 Floor[#1 (#2 - 1)] + Floor[#1 (#2 + 1)]) & @@ {1/GoldenRatio, 2 n}, {n, 100}] (* Michael De Vlieger, Oct 06 2017 *)
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PROG
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(Haskell)
a143667 n = a143667_list !! (n-1)
a143667_list = f a003849_list where
f (0:0:ws) = 0 : f ws; f (0:1:ws) = 1 : f ws; f (1:0:ws) = 2 : f ws
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CROSSREFS
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KEYWORD
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easy,nonn,word
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AUTHOR
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Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Aug 28 2008
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STATUS
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approved
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