A219071 - OEIS

%I #14 Jan 10 2018 09:01:36

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

%N Parity of pi(10^n).

%C The parity of pi(n) is obtained without calculating pi(n), and much more quickly. See the paper below.

%H Henri Lifchitz, <a href="http://www.primenumbers.net/Henri/us/ParPius.htm"> Parity of pi(n) </a>

%e For n = 3, pi(10^3) = 168 = 0 (mod 2).

%t Table[Mod[PrimePi[10^n], 2], {n, 0, 10}] (* _T. D. Noe_, Nov 13 2012 *)

%o (PARI) sq(n)=if (n<6, return(max(n-1, 0))); my(s, t); forsquarefree(i=1, sqrtint(n), t=n\i[1]^2; s+=moebius(i)*sum(i=1, sqrtint(t), t\i)); s;

%o a(n)=my(s,N=10^n); forsquarefree(i=1, logint(N, 2), s += moebius(i)*sq(sqrtnint(N, i[1]))); s%2 \\ _Charles R Greathouse IV_, Jan 10 2018

%Y Cf. A006880, A219097, A219098.

%K nonn

%O 0

%A _Henri Lifchitz_, Nov 11 2012