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A112658 Dean's Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23. 1

%I

%S 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,

%T 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,

%U 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

%N Dean's Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23.

%C Even-indexed terms of this sequence are the sequence A099545. - _Alexandre Wajnberg_, Jan 02 2006

%C 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

%H Richard A. Dean, <a href="http://www.jstor.org/stable/2313498">A sequence without repeats on x, ...</a>, Amer. Math. Monthly 72, 1965. pp. 383-385. MR 31 #350.

%H George F. McNulty, <a href="http://at.yorku.ca/cgi-bin/amca/cala-20">Avoidable Words</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F 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

%e The first few iterations of the morphism, starting with 0:

%e Start: 0

%e Rules:

%e 0 --> 01

%e 1 --> 21

%e 2 --> 03

%e 3 --> 23

%e -------------

%e 0: (#=1)

%e 0

%e 1: (#=2)

%e 01

%e 2: (#=4)

%e 0121

%e 3: (#=8)

%e 01210321

%e 4: (#=16)

%e 0121032101230321

%e 5: (#=32)

%e 01210321012303210121032301230321

%e 6: (#=64)

%e 0121032101230321012103230123032101210321012303230121032301230321

%e /* _Joerg Arndt_, Jul 18 2012 */

%t Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {0, 3}, 3 -> {2, 3}}] &, {0}, 7] (* _Robert G. Wilson v_, Dec 27 2005 *)

%K nonn

%O 1,3

%A _Jeremy Gardiner_, Dec 27 2005

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Last modified June 20 10:13 EDT 2019. Contains 324234 sequences. (Running on oeis4.)