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A288926
1-limiting word of the mapping 00->1000, 10->0001, starting with 00.
4
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
1000
00011000
10000100011000
00011000000011000100011000
100001000110001000100010001100000011000100011000
The 1-limiting word is the limit of the n-th iterates for n == 1 mod 2.
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.
LINKS
EXAMPLE
The first three iterates for n == 1 mod 2:
1000
10000100011000
100001000110001000100010001100000011000100011000
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[53]] - 48 (* A288926 *)
Flatten[Position[st, 0]] (* A288927 *)
Flatten[Position[st, 1]] (* A288928 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)
CROSSREFS
Cf. A288710 (0-limiting word), A288927, A288928, A288925.
Sequence in context: A378215 A288220 A173856 * A373840 A027356 A361114
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 25 2017
STATUS
approved