OFFSET
1
COMMENTS
The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A288996.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first six iterates of the mapping:
00
0010
0010000
001000000100
0010000001000100010010
001000000100010001001000100100010010000
00100000010001000100100010010001001000000100000010010001001000000100
MATHEMATICA
z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A288991 *)
Flatten[Position[st, 0]] (* A288992 *)
Flatten[Position[st, 1]] (* A288993 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A288996 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 25 2017
STATUS
approved