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A293945 Orbit of word "2" under De Mol's 5-shift tag system over the alphabet {1,2} defined in the Comments. 1
2, 222, 21222, 1221222, 222112, 21221222, 2221221222, 212221221222, 12212221221222, 2212212222112, 122221121221222, 11212212222112, 2122221122112, 211221121221222, 11212212221221222, 2122212212222112, 122122221121221222, 22211212212222112, 2122122221121221222, 222211212212221221222 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This tag system maps a word w over {1,2} to w', where if w begins with 1, w' is obtained by appending 2112 to w and deleting the first five letters, or if w begins with 2, w' is obtained by appending 1221222 to w and deleting the first five letters.

It can be shown that under this tag system every word different from "1" has an infinite orbit [De Mol, p. 307].

LINKS

Table of n, a(n) for n=1..20.

Liesbeth De Mol, Tracing unsolvability. A historical, mathematical and philosophical analysis with a special focus on tag systems, Ph.D. Thesis, Universiteit Gent. See page 307.

MAPLE

with(StringTools);

f1:=proc(w) local L, t2, t1, ws, w2;

t1:="2112"; t2:="1221222"; ws:=convert(w, string);

if ws[1]="1" then w2:=Join([ws, t1], ""); else w2:=Join([ws, t2], ""); fi;

L:=length(w2); if L <= 3 then return(-1); fi;

w2[6..L]; end;

# and apply f1 repeatedly to "2"

CROSSREFS

Cf. A284116, A290741, A290742.

Sequence in context: A332568 A274466 A307511 * A078276 A117076 A132936

Adjacent sequences:  A293942 A293943 A293944 * A293946 A293947 A293948

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 23 2017

STATUS

approved

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Last modified April 9 06:25 EDT 2020. Contains 333343 sequences. (Running on oeis4.)