A189166 - OEIS

%I #13 Nov 07 2025 19:03:56

%S 1,1,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,

%T 1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,1,1,0,1,0,1,0,

%U 0,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,1,0

%N Zero-one sequence based on the sequence n(n+2):  a(A005563(k))=a(k); a(A183299(k))=1-a(k), a(1)=1, a(2)=1.

%t u[n_] := n(n+2);  (*A005563*)

%t a[1] = 0; a[2]=0; h = 128;

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

%t d = (Complement[Range[Max[#1]], #1] &)[c]; (*A183299*)

%t Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189166*)

%t Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189166*)

%t Flatten[Position[%, 0]]  (*A189167*)

%t Flatten[Position[%%, 1]] (*A189168*)

%o (Python)

%o from functools import lru_cache

%o from math import isqrt

%o @lru_cache(maxsize=None)

%o def A189166(n): return 1 if n<=2 else A189166(m) if n==(k:=(m:=isqrt(n))*(m+2)) else A189166(n-m+(n<=k))^1 # _Chai Wah Wu_, Nov 07 2025

%Y Cf. A188967, A189167, A189168, A189169.

%K nonn

%O 1

%A _Clark Kimberling_, Apr 17 2011

%E Name corrected by _Chai Wah Wu_, Nov 07 2025