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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 (list; graph; refs; listen; history; text; internal format)
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

Clark Kimberling, Table of n, a(n) for n = 1..10000

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: A300477 A228495 A284683 * A030213 A187969 A132151

Adjacent sequences:  A288670 A288671 A288672 * A288674 A288675 A288676

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 15 2017

STATUS

approved

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Last modified November 28 10:16 EST 2021. Contains 349401 sequences. (Running on oeis4.)