A188973 - OEIS

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A188973

Zero-one sequence based on squares: a(A000290(k))=a(k); a(A000037(k))=1-a(k); a(1)=0.

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

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OFFSET

COMMENTS

Let u=A000290 and v=A000037, so that u(n)=n^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).

LINKS

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

MATHEMATICA

u[n_] := n^2; (*A000290*)

a[1] = 0; h = 128;

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

d = (Complement[Range[Max[#1]], #1] &)[c]; (*A000037*)

Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}];

Table[a[c[[n]]] = a[n], {n, 1, h}] (*A188973*)

Flatten[Position[%, 0]] (*A188974*)

Flatten[Position[%%, 1]] (*A188975*)

CROSSREFS