A189135 Zero-one sequence based on the central polygonal numbers n^2-n+1: a(A002061(k))=a(k); a(A135668(k))=1-a(k), a(1)=0.

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

Offset

1

Links

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

Mathematica

u[n_] := n^2-n+1;  (*A002061*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[2h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A135668*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189135*)
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189135*)
Flatten[Position[%, 0]]  (*A189136*)
Flatten[Position[%%, 1]] (*A189137*)

Crossrefs

Cf. A188967, A189136, A189137, A189133, A002061, A135668.

Sequence in context: A285565 A188076 A189011 * A369961 A219189 A029691

Adjacent sequences: A189132 A189133 A189134 * A189136 A189137 A189138

Keyword

nonn

Author

Clark Kimberling, Apr 17 2011

Status

approved