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A288673
2-limiting word of the mapping 00->0110, 10->000, starting with 00.
4
0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 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, 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, 0
OFFSET
1
COMMENTS
Iterates of the mapping, starting with 00:
00
0110
01000
00000110
0110011001000
010000100000000110
00000110000001100110011001000
01100110010000110011001000010000100000000110
The 2-limiting word is the limit of the n-th iterates for n == 2 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 two n-th iterates for n == 2 mod 3 are
01000
010000100000000110
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[14]] - 48 (* A288673 *)
Flatten[Position[st, 0]] (* A288674 *)
Flatten[Position[st, 1]] (* A288675 *)
CROSSREFS
Cf. A288665 (0-limiting word), A288670 (2-limiting word), A288674, A288675.
Sequence in context: A356982 A284683 A369968 * A030213 A187969 A132151
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 15 2017
STATUS
approved