|
%I #7 Apr 06 2020 19:40:33
%S 0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,1,
%T 0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,
%U 1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0
%N 0-limiting word of the mapping 00->0110, 1->01, starting with 00.
%C Iterates, starting with 00:
%C 00
%C 0110
%C 001010
%C 0110010010
%C 001010110010110010
%C 01100100100101011001001010110010
%C 0010101100101100101100100100101011001011001001001010110010
%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288465(n).
%H Clark Kimberling, <a href="/A288622/b288622.txt">Table of n, a(n) for n = 1..10000</a>
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "1" -> "01"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[10]] - 48 (* A288622 *)
%t Flatten[Position[st, 0]] (* A288623 *)
%t Flatten[Position[st, 1]] (* A288624 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A288465 conjectured *)
%Y Cf. A288623, A288624, A288465.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 14 2017
|
