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A288991
Fixed point of the mapping 00->0010, 01->001, 10->000, starting with 00.
5
0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0
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
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