A293945 Orbit of word "2" under De Mol's 5-shift tag system over the alphabet {1,2} defined in the Comments.

2, 222, 21222, 1221222, 222112, 21221222, 2221221222, 212221221222, 12212221221222, 2212212222112, 122221121221222, 11212212222112, 2122221122112, 211221121221222, 11212212221221222, 2122212212222112, 122122221121221222, 22211212212222112, 2122122221121221222, 222211212212221221222

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

Michael S. Branicky, Table of n, a(n) for n = 1..1025

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"

Prog

(Python)
from itertools import islice
def agen(w="2"):
    while True:
        yield int(w)
        w += ("2112" if w[0] == "1" else "1221222")
        w = w[5:]
print(list(islice(agen(), 20))) # Michael S. Branicky, Jan 06 2025

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