A288463 Positions of 0 in A288462; complement of A288464.

1, 3, 4, 6, 9, 10, 12, 14, 15, 17, 20, 21, 23, 24, 26, 29, 30, 32, 34, 35, 37, 40, 41, 43, 46, 47, 49, 51, 52, 54, 57, 58, 60, 61, 63, 66, 67, 69, 71, 72, 74, 77, 78, 80, 82, 83, 85, 88, 89, 91, 92, 94, 97, 98, 100, 102, 103, 105, 108, 109, 111, 114, 115

Offset

1,2

Comments

Conjecture: a(n)/n->1.83..., and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.

The constant 1.83... in the conjecture, psi, is the real zero of the polynomial x^3-x^2-x-1, and the conjectured inequality follows from the more precise statement -2 <= floor(psi*n) - a(n) <= 2; this can be proved with the Walnut theorem-prover. - Jeffrey Shallit, Oct 03 2025

Links

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

Lubomíra Dvořáková, Edita Pelantová, and Jeffrey Shallit, On a sequence of Kimberling and its relationship to the Tribonacci word, arXiv:2510.11318 [math.CO], 2025.

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "10"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288462 *)
Flatten[Position[st, 0]]  (* A288463 *)
Flatten[Position[st, 1]]  (* A288464 *)

Crossrefs

Cf. A288462, A288464.

Sequence in context: A082692 A032706 A153464 * A189297 A350977 A047231

Adjacent sequences: A288460 A288461 A288462 * A288464 A288465 A288466

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2017

Status

approved