A288382 Positions of 0 in A288381; complement of A288383.

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

Links

Table of n, a(n) for n=1..27.

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

Cf. A288381, A288383.

Sequence in context: A173404 A325473 A213710 * A052968 A206720 A018067

Adjacent sequences: A288379 A288380 A288381 * A288383 A288384 A288385

Keyword

nonn,easy

Author

Clark Kimberling, Jun 10 2017

Status

approved