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 A086713 A squarefree 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS f is a "squarefree morphism"; i.e. f(s) is squarefree iff s is squarefree. 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. REFERENCES Jean Berstel and Christophe Reutenauer, Squarefree words, p. 31. M. Lothaire, Combinatorics on Words, Cambridge University Press, 1997. LINKS EXAMPLE f(f(0))=01201020121021202101201020121 MATHEMATICA 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}]]] CROSSREFS Sequence in context: A194942 A129688 A309011 * A275730 A049771 A158944 Adjacent sequences:  A086710 A086711 A086712 * A086714 A086715 A086716 KEYWORD easy,nonn AUTHOR Claude Lenormand (claude.lenormand(AT)free.fr), Jul 29 2003 EXTENSIONS Edited by Dean Hickerson, Oct 19 2003 STATUS approved

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Last modified April 13 00:24 EDT 2021. Contains 342934 sequences. (Running on oeis4.)