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A288596
Fixed point of the mapping 00->0101, 10->1000, starting with 00.
4
0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0
OFFSET
1
LINKS
EXAMPLE
Iterates, starting with 00:
00
0101
010001
0100001011
0100001010100011
0100001010100010001000010111
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288599(n).
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "1000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A288596 *)
Flatten[Position[st, 0]] (* A288597 *)
Flatten[Position[st, 1]] (* A288598 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288599 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 14 2017
EXTENSIONS
Definition corrected by Georg Fischer, May 28 2021
STATUS
approved