

A288596


Fixed point of the mapping 00>0101, 10>1000, starting with 00.


4



0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0
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OFFSET

1


LINKS

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


EXAMPLE

Iterates, starting with 00:
00
0101
010001
0100001011
0100001010100011
0100001010100010001000010111
Conjecture: the number of letters (0's and 1's) in the nth iterate is given by A288599(n).


MATHEMATICA

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n  1], {"00" > "0101", "10" > "1000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]]  48 (* A288596 *)
Flatten[Position[st, 0]] (* A288597 *)
Flatten[Position[st, 1]] (* A288598 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288599 conjectured *)


CROSSREFS

Cf. A288597, A288598, A288599.
Sequence in context: A187969 A132151 A238469 * A284745 A103588 A153638
Adjacent sequences: A288593 A288594 A288595 * A288597 A288598 A288599


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jun 14 2017


EXTENSIONS

Definition corrected by Georg Fischer, May 28 2021


STATUS

approved



