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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 16 15:15 EDT 2022. Contains 353706 sequences. (Running on oeis4.)