OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
0001000
100000001000
0001000100010000001000
10000000100000010000001000100000001000
The 1-limiting word is the limit of the n-th iterates for odd n.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287439(n), for n >= 0.
See comments of A287372 for a proof of this conjecture. - Michel Dekking, Mar 19 2018
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first three n-th iterates for odd n:
1000
100000001000
10000000100000010000001000100000001000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48 (* A287457 *)
Flatten[Position[st, 0]] (* A287519 *)
Flatten[Position[st, 1]] (* A287186 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A287439 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 17 2017
STATUS
approved