login
A189011
Zero-one sequence based on triangular numbers: a(A000217(k))=a(k); a(A014132(k))=1-a(k); a(1)=0.
4
0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1
OFFSET
1
EXAMPLE
Let u=A000217 and v=A014132, so that u(n)=n(n+1)/2 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_] := n(n+1)/2; (*A000217*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A014132*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];
Table[a[c[[n]]] = a[n], {n, 1, h}] (*A189011*)
Flatten[Position[%, 0]] (*A189012*)
Flatten[Position[%%, 1]] (*A189013*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 15 2011
STATUS
approved