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A290742 Orbit of word "1" under the 3-shift tag system over the alphabet {1,2} defined in the Comments. 3

%I

%S 1,12,112,2112,21221222,212221221222,2212212221221222,

%T 22122212212221221222,222122122212212221221222,

%U 1221222122122212212221221222,12221221222122122212212222112,212212221221222122122221122112,2122212212221221222211221121221222

%N Orbit of word "1" 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].

%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 "1"

%Y Cf. A284116, A290741.

%K nonn

%O 1,2

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

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Last modified October 16 09:02 EDT 2021. Contains 348041 sequences. (Running on oeis4.)