OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
00011000
10000100011000
00011000000011000100011000
100001000110001000100010001100000011000100011000
The 0-limiting word is the limit of the n-th iterates for n == 0 mod 2.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first three iterates for n == 0 mod 2:
00
00011000
00011000000011000100011000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[54]] - 48 (* A288710 *)
Flatten[Position[st, 0]] (* A288711 *)
Flatten[Position[st, 1]] (* A288755 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 24 2017
STATUS
approved