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A286807 Fixed point of the mapping 00->001, 1->101, starting with 00. 3
0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Conjecture: The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A132045.
LINKS
EXAMPLE
Iterates, starting with 00:
00
001
001101
0011011010101
0011011010101101010101010101
00110110101011010101010101011010101010101010101010101010101
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "101"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A286807 *)
Flatten[Position[st, 0]] (* A286808 *)
Flatten[Position[st, 1]] (* A286809 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A132045 conjectured *)
CROSSREFS
Sequence in context: A181712 A288729 A335617 * A126564 A180433 A358771
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2017
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)