A101565 - OEIS

%I #10 Oct 01 2018 03:30:11

%S 1,0,0,1,0,2,2,0,1,2,2,2,2,0,2,1,0,4,2,2,2,0,0,2,3,0,2,0,0,4,2,0,0,2,

%T 2,5,2,0,0,2,2,0,0,2,2,2,2,2,1,2,2,2,0,6,0,-2,0,2,2,4,2,0,0,1,0,2,2,2,

%U 4,2,0,6,2,0,0,2,0,4,2,2,5,0,0,2,2,2,2,2,0,4,2,0,2,0,0,2,2,-2,2,5,0

%N a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*[(n+1) mod (k+1) = 0], where [] denotes the Iverson bracket.

%o (PARI) tm(n) = hammingweight(n)%2;

%o a(n) = sum(k=0, n, if (((n+1) % (k+1))==0, (-1)^tm(n-k))); \\ _Michel Marcus_, Oct 01 2018

%Y Cf. A010060 (Thue-Morse sequence).

%K easy,sign

%O 0,6

%A _Paul Barry_, Dec 07 2004