OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288465(n).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
Iterates, starting with 00:
00
0101
010010
0100101100
010010110010100101
01001011001010010110010010110010
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "10"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A288462 *)
Flatten[Position[st, 0]] (* A288463 *)
Flatten[Position[st, 1]] (* A288464 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288465 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 11 2017
STATUS
approved