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 A112658 Dean's Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23. 1
 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Even-indexed terms of this sequence are the sequence A099545. - Alexandre Wajnberg, Jan 02 2006 Fractal sequence: odd terms are 0, 2, 0, 2,...; the subsets formed with the terms of index (2^i)n, with i>0, are identical: a(2n)=a(4n)=a(8n)=a(16n)=... - Alexandre Wajnberg, Jan 02 2006 LINKS Richard A. Dean, A sequence without repeats on x, ..., Amer. Math. Monthly 72, 1965. pp. 383-385. MR 31 #350. George F. McNulty, Avoidable Words FORMULA It should be easy to prove that a(4n) = 0, a(4n+2) = 2, a(8n+1) = 1, a(8n+5) = 3, a(4n+3) = a(2n+1). This would imply that a(2n) = 2(n mod 2), a(2n+1) = 1 + 2*A014707(n), with A014707(n) the classical paperfolding curve. - Ralf Stephan, Dec 28 2005 EXAMPLE The first few iterations of the morphism, starting with 0: Start: 0 Rules:   0 --> 01   1 --> 21   2 --> 03   3 --> 23 ------------- 0:   (#=1)   0 1:   (#=2)   01 2:   (#=4)   0121 3:   (#=8)   01210321 4:   (#=16)   0121032101230321 5:   (#=32)   01210321012303210121032301230321 6:   (#=64)   0121032101230321012103230123032101210321012303230121032301230321 /* Joerg Arndt, Jul 18 2012 */ MATHEMATICA Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {0, 3}, 3 -> {2, 3}}] &, {0}, 7] (* Robert G. Wilson v, Dec 27 2005 *) CROSSREFS Sequence in context: A177351 A117901 A074984 * A190693 A257571 A219649 Adjacent sequences:  A112655 A112656 A112657 * A112659 A112660 A112661 KEYWORD nonn AUTHOR Jeremy Gardiner, Dec 27 2005 STATUS approved

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Last modified May 25 11:17 EDT 2019. Contains 323539 sequences. (Running on oeis4.)