The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293945 Orbit of word "2" under De Mol's 5-shift 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)



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].


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.



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"


Cf. A284116, A290741, A290742.

Sequence in context: A332568 A274466 A307511 * A078276 A117076 A132936

Adjacent sequences:  A293942 A293943 A293944 * A293946 A293947 A293948




N. J. A. Sloane, Oct 23 2017



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 9 06:25 EDT 2020. Contains 333343 sequences. (Running on oeis4.)