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A288382
Positions of 0 in A288381; complement of A288383.
4
1, 2, 3, 5, 8, 13, 22, 39, 72, 137, 266, 523, 1036, 2061, 4110, 8207, 16400, 32785, 65554, 131091, 262164, 524309, 1048598, 2097175, 4194328, 8388633, 16777242
OFFSET
1,2
COMMENTS
a(n+1)/a(n)-> 2.
Appears to be the same as A052968 (apart from the offset). - R. J. Mathar, Jun 14 2017
This conjecture is proved in A288381. - Michel Dekking, Feb 18 2021
FORMULA
a(n) = -1 + A288133(n-1) for n >= 2.
Conjectures from Colin Barker, Jun 10 2017: (Start)
G.f.: x*(1 - 2*x + x^3 - x^4) / ((1 - x)^2*(1 - 2*x)).
a(n) = -1 + 2^(n-3) + n for n>2.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>5.
(End)
Barker's conjectures are implied by Mathar's conjecture. - Michel Dekking, Feb 18 2021
MATHEMATICA
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0001", "1" -> "11"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A288381 *)
Flatten[Position[st, 0]] (* A288382 *)
Flatten[Position[st, 1]] (* A288383 *)
CROSSREFS
Sequence in context: A173404 A325473 A213710 * A052968 A206720 A018067
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 10 2017
STATUS
approved