%I #32 Mar 15 2022 12:31:36

%S 2,21222,221221222,2212221221222,22212212221221222,

%T 122122212212221221222,1222122122212212222112,21221222122122221122112,

%U 212221221222211221121221222,2212212222112211212212221221222,22122221122112122122212212221221222,222211221121221222122122212212221221222

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

%C 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.

%C This is a 3-shift version of a 5-shift tag system studied in [De Mol, p. 307] (cf. A293945).

%H Michael S. Branicky, <a href="/A290741/b290741.txt">Table of n, a(n) for n = 1..328</a>

%H Liesbeth De Mol, <a href="http://www.clps.ugent.be/sites/default/files/publications/dissertation.pdf">Tracing unsolvability. A historical, mathematical and philosophical analysis with a special focus on tag systems</a>, Ph.D. Thesis, Universiteit Gent. See page 307.

%p with(StringTools);

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

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

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

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

%p w2[4..L]; end;

%p # and apply f1 repeatedly to "2"

%o (Python)

%o from itertools import islice

%o def agen(w="2"):

%o while True:

%o yield int(w)

%o w += ("2112" if w[0] == "1" else "1221222")

%o w = w[3:]

%o print(list(islice(agen(), 12))) # _Michael S. Branicky_, Mar 15 2022

%Y Cf. A284116, A290742, A293945.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Aug 11 2017

%E Definition corrected by _N. J. A. Sloane_, Oct 23 2017 (this is not De Mol's 5-shift tag system, which is described in A293945).