|
%I #9 Apr 07 2020 21:47:42
%S 0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,
%T 0,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,
%U 0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,1
%N 1-limiting word of the mapping 00->0101, 10->010, starting with 00.
%C Iterates, starting with 00:
%C 00
%C 0101
%C 00101
%C 01010101
%C 00100100101
%C 0101010001000101
%C 0010010010010101001010101
%C 010101000100010001001001000100100101
%C The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.
%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288523(n).
%H Clark Kimberling, <a href="/A288524/b288524.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 4 odd-numbered iterates:
%e 0101
%e 01010101
%e 0101010001000101
%e 010101000100010001001001000100100101
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "010"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[19]] - 48 (* A288524 *)
%t Flatten[Position[st, 0]] (* A288525 *)
%t Flatten[Position[st, 1]] (* A288526 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A288523 conjectured *)
%Y Cf. A288525, A288526, A288523.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 14 2017
|
