A284121 - OEIS

%I #28 Apr 19 2018 13:06:03

%S 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 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 6,1,6,6,6,6,1,6,6,6,1,6,6,6,1,10,1,10,6,6

%N 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 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 The empty word is included in the count.

%C 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 Lars Blomberg, <a href="/A284121/b284121.txt">Table of n, a(n) for n = 1..6075</a>

%H 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 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 Cf. A284116, A284119, A291792, A291793.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Mar 20 2017

%E Edited by _N. J. A. Sloane_, Jul 29 2017

%E a(50)-a(83) from _Lars Blomberg_, Sep 08 2017