A189084 - OEIS

A189084

Zero-one sequence based on floor(sqrt(3)): a(A022838(k))=a(k); a(A054406(k))=1-a(k); a(1)=0.

0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

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OFFSET

LINKS

Table of n, a(n) for n=1..135.

EXAMPLE

Let u=A022838=(Beatty sequence for sqrt(3)) and v=A054406=(complement of u). Then A189084 is the sequence a given by a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

MATHEMATICA

r=3^(1/2); u[n_] := Floor[n*r]; (*A022838*)

a[1] = 0; h = 128;

c = (u[#1] &) /@ Range[2h];

d = (Complement[Range[Max[#1]], #1] &)[c]; (*A054406*)

Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189084*)

Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189084*)

Flatten[Position[%, 0]] (*A189085*)

Flatten[Position[%%, 1]] (*A189086*)

CROSSREFS

Cf. A188967, A189085, A189086.

Sequence in context: A215581 A156595 A286493 * A143222 A286490 A372728