OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0011000
100010011000
0011000001010011000
1000100110001000001001010011000
0011000001010011000001100010000010001001010011000
The 0-limiting word is the limit of the n-th iterates for even n.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287525(n), for n >= 0.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first four n-th iterates for even n:
00
0011000
0011000001010011000
0011000001010011000001100010000010001001010011000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48 (* A287382 *)
Flatten[Position[st, 0]] (* A287440 *)
Flatten[Position[st, 1]] (* A287448 *)
v = Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 18 2017
STATUS
approved