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A289128
Fixed point of the mapping 00->0010, 01->011, 10->010, starting with 00.
5
0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289131.
LINKS
EXAMPLE
The first six iterates of the mapping:
00
0010
0010010
00100100110
001001001100101010
0010010011001010100110110110
MATHEMATICA
z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "011", "10" -> "010"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48 (* A289128 *)
Flatten[Position[st, 0]] (* A289129 *)
Flatten[Position[st, 1]] (* A289130 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289131 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 28 2017
STATUS
approved