login
A286059
Fixed point of the mapping 00->001, 1->011, starting with 00.
5
0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1
OFFSET
1
COMMENTS
Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A286062.
LINKS
EXAMPLE
Iterates, starting with 00:
00
001
001011
0010110011011
00101100110110010110110011011
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A286059 *)
Flatten[Position[st, 0]] (* A286060 *)
Flatten[Position[st, 1]] (* A286061 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A286062 conjectured *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2017
STATUS
approved