A288670 - OEIS

A288670

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

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

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OFFSET

COMMENTS

Iterates of the mapping, starting with 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

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

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 *)