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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
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

Table of n, a(n) for n=1..13.

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[4..L]; end;

# and apply f1 repeatedly to "1"

CROSSREFS

Cf. A284116, A290741.

Sequence in context: A265948 A016152 A089700 * A268767 A221368 A083767

Adjacent sequences:  A290739 A290740 A290741 * A290743 A290744 A290745

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 11 2017

STATUS

approved

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Last modified February 24 10:37 EST 2020. Contains 332209 sequences. (Running on oeis4.)