cp's OEIS Frontend

A284121 Period of orbit of Post's tag system applied to the word (100)^n (version 1), or -1 if the orbit increases without limit.

%I A284121 #28 Apr 19 2018 13:06:03
%S A284121 2,6,6,6,1,10,28,6,10,6,6,6,1,1,6,28,10,6,10,6,6,1,6,6,1,6,6,6,6,6,6,
%T A284121 52,6,6,6,6,6,6,6,6,6,6,6,28,6,1,1,28,6,6,6,6,6,1,6,6,6,10,6,6,6,6,1,
%U A284121 6,1,6,6,6,6,1,6,6,6,1,6,6,6,1,10,1,10,6,6
%N A284121 Period of orbit of Post's tag system applied to the word (100)^n (version 1), or -1 if the orbit increases without limit.
%C A284121 Post's tag system maps a word w over {0,1} to w', where if w begins with 0, w' is obtained by appending 00 to w and deleting the first three letters, or if w begins with 1, w' is obtained by appending 1101 to w and deleting the first three letters.
%C A284121 The empty word is included in the count.
%C A284121 Here a(n)=1 if the orbit ends at the empty word. On the other hand, Asveld defines a(n) to be zero if that happens, which gives a different sequence, A291793. - _N. J. A. Sloane_, Sep 04 2017
%H A284121 Lars Blomberg, <a href="/A284121/b284121.txt">Table of n, a(n) for n = 1..6075</a>
%H A284121 Peter R. J. Asveld, <a href="http://doc.utwente.nl/66184/1/1988m20.pdf">On a Post's System of Tag</a>. Bulletin of the EATCS 36 (1988), 96-102.
%e A284121 For n = 2 the orbit of (100)^2 = 100100 consists of a preperiod of length 15, followed by a periodic portion of length 6. So a(2) = 6.
%Y A284121 Cf. A284116, A284119, A291792, A291793.
%K A284121 nonn
%O A284121 1,1
%A A284121 _Jeffrey Shallit_, Mar 20 2017
%E A284121 Edited by _N. J. A. Sloane_, Jul 29 2017
%E A284121 a(50)-a(83) from _Lars Blomberg_, Sep 08 2017