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Search: id:A086713
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| A086713 |
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A square-free sequence: define a mapping from the set of strings over the alphabet {0,1,2} by f(0)=01201, f(1)=020121, f(2)=0212021 and f of the concatenation of s and t is the concatenation of f(s) and f(t). Then each of 0, f(0), f(f(0)), ... is an initial substring of the next; their limit is the infinite sequence given above. |
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| 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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f is a "square-free morphism"; i.e. f(s) is square-free iff s is square-free.
For any i>0, f^i(0) has the same number of 0's and 1's and one less 2. The length of f^i(0) is A083066(i) = (4*6^i + 1)/5.
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REFERENCES
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Jean Berstel and Christophe Reutenauer, Square-free words, p. 31.
M. Lothaire, Combinatorics on Words, Cambridge University Press, 1997.
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EXAMPLE
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f(f(0))=01201020121021202101201020121
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MATHEMATICA
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f[s_] := Flatten[{{0, 1, 2, 0, 1}, {0, 2, 0, 1, 2, 1}, {0, 2, 1, 2, 0, 2, 1}}[[ #+1]]&/@s]; f[f[f[{0}]]]
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CROSSREFS
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Sequence in context: A035232 A091603 A129688 this_sequence A049771 A139366 A049767
Adjacent sequences: A086710 A086711 A086712 this_sequence A086714 A086715 A086716
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KEYWORD
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easy,nonn
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Jul 29 2003
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Oct 19 2003
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