A219097 Parity of pi(2^n).

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, 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, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0

Offset

0

Comments

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

Links

Table of n, a(n) for n=0..91.

Henri Lifchitz, Parity of pi(n)

Formula

a(n) = A000035(A007053(n)). - David Baugh, Nov 06 2020

Example

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

Maple

A071986 := proc(n)
    numtheory[pi](n) mod 2 ;
end proc:
A219097 := proc(n)
    A071986(2^n) ;
end proc: # R. J. Mathar, Nov 12 2012

Mathematica

Table[Mod[PrimePi[2^n], 2], {n, 32}] (* Alonso del Arte, Nov 12 2012 *)

Crossrefs

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

Sequence in context: A374413 A260446 A096268 * A284751 A288426 A286052

Adjacent sequences: A219094 A219095 A219096 * A219098 A219099 A219100

Keyword

nonn

Author

Henri Lifchitz, Nov 11 2012

Extensions

a(91) from David Baugh, Nov 06 2020

Status

approved