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A289057
Fixed point of the mapping 00->0010, 01->010, 10->011, starting with 00.
5
0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1
OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289060.
LINKS
EXAMPLE
First eight iterates of the mapping:
00
0010
0010011
00100110101
00100110100110111
0010011010011011010011111
001001101001101101001110110110101111
001001101001101101001110110110101011101110110111111
MATHEMATICA
z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "011"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A289057 *)
Flatten[Position[st, 0]] (* A289058 *)
Flatten[Position[st, 1]] (* A289059 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289060 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 27 2017
STATUS
approved