

A290741


Orbit of word "2" under the 3shift tag system over the alphabet {1,2} defined in the Comments.


3



2, 21222, 221221222, 2212221221222, 22212212221221222, 122122212212221221222, 1222122122212212222112, 21221222122122221122112, 212221221222211221121221222, 2212212222112211212212221221222, 22122221122112122122212212221221222, 222211221121221222122122212212221221222
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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 three letters, or if w begins with 2, w' is obtained by appending 1221222 to w and deleting the first three letters.
This is a 3shift version of a 5shift tag system studied in [De Mol, p. 307] (cf. A293945).


LINKS

Table of n, a(n) for n=1..12.
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[4..L]; end;
# and apply f1 repeatedly to "2"


CROSSREFS

Cf. A284116, A290742, A293945.
Sequence in context: A214598 A242959 A123692 * A261362 A132942 A237521
Adjacent sequences: A290738 A290739 A290740 * A290742 A290743 A290744


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Aug 11 2017


EXTENSIONS

Definition corrected by N. J. A. Sloane, Oct 23 2017 (this is not De Mol's 5shift tag system, which is described in A293945).


STATUS

approved



