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A288670
1-limiting word of the mapping 00->0110, 10->000, starting with 00.
4
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
0110
01000
00000110
0110011001000
010000100000000110
00000110000001100110011001000
01100110010000110011001000010000100000000110
The 1-limiting word is the limit of the n-th iterates for n == 1 mod 3. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).
LINKS
EXAMPLE
The first three n-th iterates for n == 1 mod 3 are
0110
0110011001000
01100110010000110011001000010000100000000110
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[13]] - 48 (* A288670 *)
Flatten[Position[st, 0]] (* A288671 *)
Flatten[Position[st, 1]] (* A288672 *)
CROSSREFS
Cf. A288665 (0-limiting word), A288671, A288672, A288673 (2-limiting word).
Sequence in context: A287657 A347198 A079336 * A057215 A284905 A291197
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 15 2017
STATUS
approved