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A288926 1-limiting word of the mapping 00->1000, 10->0001, starting with 00. 4
1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

00011000

10000100011000

00011000000011000100011000

100001000110001000100010001100000011000100011000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 2.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.

LINKS

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

EXAMPLE

The first three iterates for n == 1 mod 2:

1000

10000100011000

100001000110001000100010001100000011000100011000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]

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

st = ToCharacterCode[w[53]] - 48 (* A288926 *)

Flatten[Position[st, 0]] (* A288927 *)

Flatten[Position[st, 1]] (* A288928 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)

CROSSREFS

Cf. A288710 (0-limiting word), A288927, A288928, A288925.

Sequence in context: A322075 A288220 A173856 * A027356 A181663 A247223

Adjacent sequences: A288923 A288924 A288925 * A288927 A288928 A288929

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 25 2017

STATUS

approved

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Last modified November 29 09:15 EST 2022. Contains 358422 sequences. (Running on oeis4.)