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 A073058 Define s(1)={1,2}, s(2)={1,3} and s(3)={1}. For a finite sequence A={a_1, ..., a_n}, with elements in {1,2,3}, define t(A) to be the concatenation of A, s(a_1), s(a_2), ... and s(a_n). Start with the sequence {1,2,3} and repeatedly apply t; limiting sequence is shown. 25
 1, 2, 3, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A fractal sequence related to a sequence of Rauzy. LINKS P. Arnoux and E. Harriss, What is a Rauzy Fractal?, Notices Amer. Math. Soc., 61 (No. 7, 2014), 768-770, also p. 704 and front cover. Vincent Canterini and Anne Siegel, Geometric Representations of Substitutions of Pisot Type, Trans. Amer. Math. Soc. 353 (2001), 5121-5144. MATHEMATICA s[1]={1, 2}; s[2]={1, 3}; s[3]={1}; t[a_] := Join[a, Flatten[s/@a]]; t[t[t[t[{1, 2, 3}]]]] (* Continue applying t for more terms *) Nest[ Flatten[ Join[#, # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}}]] &, {1, 2, 3}, 4] (* Robert G. Wilson v, Jan 01 2017 *) CROSSREFS Cf. A092782, A103684, A105083, A245553, A245554. Sequence in context: A190496 A193926 A211450 * A100336 A275609 A006376 Adjacent sequences:  A073055 A073056 A073057 * A073059 A073060 A073061 KEYWORD nonn AUTHOR Roger L. Bagula, Aug 16 2002 STATUS approved

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