A189031 Zero-one sequence based on the sequence (6n-5): a(A016921(k))=a(k); a(A114024(k))=1-a(k); a(1)=0.

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

Offset

1

Links

Table of n, a(n) for n=1..128.

Example

Let u=A016921 and v=A114024, so that u(n)=6n-5 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).

Mathematica

u[n_] := 6n-5;  (*A016921*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A114024*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189031*)
Flatten[Position[%, 0]]  (*A189032*)
Flatten[Position[%%, 1]] (*A189033*)

Crossrefs

Cf. A188967, A189032, A189033.

Sequence in context: A190204 A189028 A301850 * A189212 A147781 A327216

Adjacent sequences: A189028 A189029 A189030 * A189032 A189033 A189034

Keyword

nonn

Author

Clark Kimberling, Apr 15 2011

Status

approved