

A293945


Orbit of word "2" under De Mol's 5shift 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



