

A290742


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


4



1, 12, 112, 2112, 21221222, 212221221222, 2212212221221222, 22122212212221221222, 222122122212212221221222, 1221222122122212212221221222, 12221221222122122212212222112, 212212221221222122122221122112, 2122212212221221222211221121221222
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


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].


LINKS



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 "1"


PROG

(Python)
from itertools import islice
def agen(w="1"):
while True:
yield int(w)
w += ("2112" if w[0] == "1" else "1221222")
w = w[3:]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



