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A288710
0-limiting word of the mapping 00->1000, 10->0001, starting with 00.
4
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 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, 0, 0, 0, 1, 1, 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 0-limiting word is the limit of the n-th iterates for n == 0 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 == 0 mod 2:
00
00011000
00011000000011000100011000
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[54]] - 48 (* A288710 *)
Flatten[Position[st, 0]] (* A288711 *)
Flatten[Position[st, 1]] (* A288755 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)
CROSSREFS
Cf. A288926 (1-limiting word), A288711, A288755, A288925.
Sequence in context: A137331 A093386 A219098 * A179827 A285133 A011658
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 24 2017
STATUS
approved