A189008 Zero-one sequence based on cubes: a(A000578(k))=a(k); a(A007412(k))=1-a(k); a(1)=0.

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

Offset

1

Comments

Let u=A000578 and v=A007412, so that u(n)=n^3 and v=complement(u) for n>=1. Then a is a self-generating zero-one sequence with initial value a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

Links

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

Mathematica

u[n_] := n^3;
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[h]; (*A000578*)
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A007412*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189008*)
Flatten[Position[%, 0]]  (*A189009*)
Flatten[Position[%%, 1]] (*A189010*)

Crossrefs

Cf. A188967, A189009, A189010.

Sequence in context: A179081 A113217 A189219 * A353681 A285515 A190204

Adjacent sequences: A189005 A189006 A189007 * A189009 A189010 A189011

Keyword

nonn

Author

Clark Kimberling, Apr 15 2011

Status

approved