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A284932
Fixed point of the mapping 00->001, 1->10, starting with 00.
7
0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0
OFFSET
1
COMMENTS
The number of letters (0's and 1's) in the n-th iterate, beginning with 2,3,5,8,13, is given by A286938, which appears to be the same as A164457 except for initial 2,3,5.
LINKS
EXAMPLE
Iterates, starting with 00:
00
001
00110
00110100
0011010010001
001101001000110001010
001101001000110001010100010100100
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "10"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A284932 *)
Flatten[Position[st, 0]] (* A285352 *)
Flatten[Position[st, 1]] (* A285303 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A286938 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 03 2017
STATUS
approved