A289671 - OEIS

%I #29 Sep 27 2019 07:50:35

%S 0,2,4,8,16,48,64,128,320,704,1536,3328,5632,9728,20480,44032,94208,

%T 180224,348160,720896,1458176,2801664,6062080,12582912,23986176,

%U 49807360,103809024,202899456,415760384,853540864,1663041536

%N Consider the Post tag system defined in A284116; a(n) = number of binary words of length n which terminate in a cycle.

%C For n such that no binary word of length n has an infinite orbit under the Post tag system (cf. A284116), which includes all n <= 57, a(n) + A289670(n) = 2^n.

%H Don Reble, <a href="/A289671/b289671.txt">Table of n, a(n) for n = 1..57</a>

%e For length n=2, there are two words which cycle, 10 and 11: 10 -> 101 -> 1101 -> 11101 -> 011101 -> 10100 -> 001101 -> 10100, which has entered a cycle.

%p See A289670.

%t Table[ne = 0;

%t For[i = 0, i < 2^n, i++, lst = {};

%t   w = IntegerString[i, 2, n];

%t   While[! MemberQ[lst, w],

%t    AppendTo[lst, w];

%t    If[w == "", ne++; Break[]];

%t    If[StringTake[w, 1] == "0", w = StringDrop[w <> "00", 3],

%t     w = StringDrop[w <> "1101", 3]]]];

%t 2^n - ne, {n, 1, 12}] (* _Robert Price_, Sep 26 2019 *)

%Y Cf. A284116, A284119, A284121, A289670-A289674.

%Y A289675 lists the initial words that terminate at the empty string.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Jul 29 2017