OFFSET
1
COMMENTS
The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289000.
Conjecture: a(n) = A171588(n+3) for all n>0. - Michel Dekking, Mar 21 2022
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
EXAMPLE
The first seven iterates of the mapping:
00
0010
0010001
001000100101
00100010010001001001
0010001001000100100100010010001001
0010001001000100100100010010001001001000100100010010001001
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" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A288997 *)
Flatten[Position[st, 0]] (* A288998 *)
Flatten[Position[st, 1]] (* A288999 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289000 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 25 2017
STATUS
approved