A189135 - OEIS

%I #6 Mar 30 2012 18:57:23

%S 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,

%T 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,

%U 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

%N 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.

%t u[n_] := n^2-n+1;  (*A002061*)

%t a[1] = 0; h = 128;

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

%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A135668*)

%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189135*)

%t Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189135*)

%t Flatten[Position[%, 0]]  (*A189136*)

%t Flatten[Position[%%, 1]] (*A189137*)

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

%K nonn

%O 1

%A _Clark Kimberling_, Apr 17 2011