A288864 - OEIS

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A288864

4-limiting word of the mapping 00->1000, 10->011, starting with 00.

0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1

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OFFSET

COMMENTS

Iterates of the mapping, starting with 00:

1000

0111000

0110111000

01011110111000

0011111011110111000

10001111011111011110111000

01110001110111111011111011110111000

011011100011011111110111111011111011110111000

The 4-limiting word is the limit of the n-th iterates for n == 4 mod 5.

The number of letters (0's and 1's) in the n-th iterate is given by A288243(n), for n >= 0.

LINKS

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

EXAMPLE

The first two n-th iterates for n == 3 mod 5:

01011110111000

010111101110001011111111011111110111111011111011110111000

(The lengths of the first 10 such iterates are 10, 45, 127, 279, 534, 947, 1594, 2573, 4018, 6126.)

MATHEMATICA

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "011"}]

Table[w[n], {n, 0, 8}]

st = ToCharacterCode[w[54]] - 48 (* A288864 *)

Flatten[Position[st, 0]] (* A288865 *)

Flatten[Position[st, 1]] (* A288866 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)

CROSSREFS

Cf. A288226 (0-limiting word), A288855 (1-limiting word), A288858 (2-limiting word), A288861 (3-limiting word), A288865, A288866, A288243.

Sequence in context: A309754 A112690 A316343 * A115971 A320007 A072165

Adjacent sequences: A288861 A288862 A288863 * A288865 A288866 A288867

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 24 2017

STATUS

approved