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A288257
Fixed point of the mapping 00->0010, 1->100, starting with 00.
4
0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0
OFFSET
1
LINKS
EXAMPLE
Iterates, starting with 00:
00
0010
00101000
0010100010000100
0010100010000100100001000101000010
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "1" -> "100"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A288257 *)
Flatten[Position[st, 0]] (* A288258 *)
Flatten[Position[st, 1]] (* A288259 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288260 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 07 2017
STATUS
approved