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A105220 Trajectory of 1 under the morphism 1->{1,2,1}, 2->{2,2,2}. 4
1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Dekking substitution for the Cantor set: characteristic polynomial = x^2 - 5*x + 6 of matrix [2, 0; 1, 3].

This substitution is useful for computing the devil's staircase by bb=aa/. 1->1/3/. 2->0 /. 3->0; ListPlot[FoldList[Plus, 0, bb], PlotRange -> All, PlotJoined -> True, Axes ->False];

The Wikipedia article on L-system Example 3 is "Cantor dust" given by the axiom: A and rules: A -> ABA, B -> BBB. This is isomorphic to the system given in the sequence name. - Michael Somos, Jan 12 2015

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..19682

F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no. 1, 1982, page 99, section 4.15

Wikipedia, L-system Example 3: Cantor dust

Index entries for sequences that are fixed points of mappings

FORMULA

a(n) = 2 - A088917(n) = 1 + A316829(n). - Antti Karttunen, Aug 24 2019

a(n) = 2 if the ternary expansion of n contains the digit 1, otherwise a(n) = 1. - Joerg Arndt, Aug 24 2019

MATHEMATICA

Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {2, 2, 2}} &], {1}, 5]]

PROG

(PARI)

A088917(n) = { while(n, if(n%3==1, return(0), n\=3)); (1); }; \\ Originally from A005823

A105220(n) = (2-A088917(n)); \\ Antti Karttunen, Aug 23 2019

CROSSREFS

Cf. A088917, A316829.

Sequence in context: A115588 A240471 A263569 * A083654 A164878 A319695

Adjacent sequences:  A105217 A105218 A105219 * A105221 A105222 A105223

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Apr 29 2005

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)