A288665 - OEIS

A288665

0-limiting word of the mapping 00->0110, 10->000, starting with 00.

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, 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, 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

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OFFSET

COMMENTS

Iterates of the mapping, starting with 00:

0110

01000

00000110

0110011001000

010000100000000110

00000110000001100110011001000

01100110010000110011001000010000100000000110

The 0-limiting word is the limit of the n-th iterates for n == 0 mod 3.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288668(n).

LINKS

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

EXAMPLE

The first three n-th iterates for n == 0 mod 3 are

00000110

00000110000001100110011001000

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[9]] - 48 (* A288665 *)

Flatten[Position[st, 0]] (* A288666 *)

Flatten[Position[st, 1]] (* A288667 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A288668 conjectured *)

CROSSREFS

Cf. A288666, A288667, A288668, A299670 (1-limiting word), A299673 (2-limiting word).

Sequence in context: A011667 A144195 A226464 * A011759 A316345 A118952

Adjacent sequences: A288662 A288663 A288664 * A288666 A288667 A288668

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 15 2017

STATUS

approved