OFFSET
1
COMMENTS
Iterates, starting with 00:
00
0101
00101
01010101
00100100101
0101010001000101
0010010010010101001010101
010101000100010001001001000100100101
The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288523(n).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first 4 odd-numbered iterates:
0101
01010101
0101010001000101
010101000100010001001001000100100101
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[19]] - 48 (* A288524 *)
Flatten[Position[st, 0]] (* A288525 *)
Flatten[Position[st, 1]] (* A288526 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288523 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 14 2017
STATUS
approved