OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289004.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first six iterates of the mapping:
00
0010
0010010
00100101000
001001010010000100
0010010100100001001000101000010
MATHEMATICA
z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "010"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A289239 *)
Flatten[Position[st, 0]] (* A289240 *)
Flatten[Position[st, 1]] (* A289241 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289004 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 29 2017
STATUS
approved