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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

Table of n, a(n) for n=1..105.

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

Index entries for sequences that are fixed points of mappings

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.)