OFFSET
1
COMMENTS
Iterates, starting with 00:
00
0101
00110011
01010110110101011011
00110011001101100110110011001100110110011011
The 0-limiting word is the limit taken over even-numbered iterations of the mapping.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288476(n).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
First three even-numbered iterates of the mapping:
00
00110011
00110011001101100110110011001100110110011011
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[10]] - 48 (* A288551 *)
Flatten[Position[st, 0]] (* A288552 *)
Flatten[Position[st, 1]] (* A288553 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 14 2017
STATUS
approved