A219097 - OEIS

%I #23 Nov 08 2020 02:30:09

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

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

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

%N Parity of pi(2^n).

%C The parity of pi(n) can be 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>

%F a(n) = A000035(A007053(n)). - _David Baugh_, Nov 06 2020

%e For n = 5 , pi(2^5) = 11 = 1 (mod 2) = 1.

%p A071986 := proc(n)

%p     numtheory[pi](n) mod 2 ;

%p end proc:

%p A219097 := proc(n)

%p     A071986(2^n) ;

%p end proc: # _R. J. Mathar_, Nov 12 2012

%t Table[Mod[PrimePi[2^n], 2], {n, 32}] (* _Alonso del Arte_, Nov 12 2012 *)

%Y Cf. A007053, A071986, A131378, A006880, A219071.

%K nonn

%O 0

%A _Henri Lifchitz_, Nov 11 2012

%E a(91) from _David Baugh_, Nov 06 2020