A288226 - OEIS

A288226

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

0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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 0-limiting word is the limit of the n-th iterates for n == 0 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 == 0 mod 5: 00 and 0011111011110111000. (The lengths of the first 10 such iterates are 2, 19, 71, 178, 366, 676, 1172, 1939, 3086, 4770.)

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[50]] - 48 (* A288226 *)

Flatten[Position[st, 0]] (* A288227 *)

Flatten[Position[st, 1]] (* A288228 *)

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

CROSSREFS

Cf. A288855 (1-limiting word), A288858 (2-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288227, A288228, A288243.

Sequence in context: A228487 A295306 A295303 * A373253 A104121 A179770

Adjacent sequences: A288223 A288224 A288225 * A288227 A288228 A288229

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2017

STATUS

approved