OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A001580.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
Iterates, starting with 00:
00
001
001010
00101000100
00101000100010010001
0010100010001001000100100010100010010
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A285666 *)
Flatten[Position[st, 0]] (* A285667 *)
Flatten[Position[st, 1]] (* A286058 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A001580 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2017
STATUS
approved