|
|
A290742
|
|
Orbit of word "1" under the 3-shift 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 3-shift version of a 5-shift 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
|
|
|
|