|
%I #6 Apr 06 2020 19:44:20
%S 0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,
%T 0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,
%U 1,1,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1
%N 0-limiting word of the mapping 00->1000, 10->0001, starting with 00.
%C Iterates of the mapping, starting with 00:
%C 00
%C 1000
%C 00011000
%C 10000100011000
%C 00011000000011000100011000
%C 100001000110001000100010001100000011000100011000
%C The 0-limiting word is the limit of the n-th iterates for n == 0 mod 2.
%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.
%H Clark Kimberling, <a href="/A288710/b288710.txt">Table of n, a(n) for n = 1..10000</a>
%e The first three iterates for n == 0 mod 2:
%e 00
%e 00011000
%e 00011000000011000100011000
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[54]] - 48 (* A288710 *)
%t Flatten[Position[st, 0]] (* A288711 *)
%t Flatten[Position[st, 1]] (* A288755 *)
%t Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)
%Y Cf. A288926 (1-limiting word), A288711, A288755, A288925.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 24 2017
|
