A295891 - OEIS

%I #7 Dec 01 2017 18:52:05

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

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

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

%N a(n) = 1 if binary weights of n and A003961(n) are of the different parity, 0 otherwise; a(n) = A010060(n) XOR A010060(A003961(n)).

%H Antti Karttunen, <a href="/A295891/b295891.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A000120(n) + A000120(A003961(n)) mod 2.

%F a(n) = 1 - A295892(n).

%F a(2n) = a(n) XOR A295890(A003961(n)) = a(n) + A295890(A003961(n)) mod 2.

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from _Michel Marcus_

%o A295891(n) = ((hammingweight(n)+hammingweight(A003961(n)))%2);

%o (Scheme) (define (A295891 n) (A000035 (+ (A000120 n) (A000120 (A003961 n)))))

%Y Cf. A000035, A000120, A003961, A010060, A295890, A295892, A295893.

%K nonn

%O 1

%A _Antti Karttunen_, Nov 30 2017