A219071 Parity of pi(10^n).

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

Offset

0

Comments

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

Links

Table of n, a(n) for n=0..28.

Henri Lifchitz, Parity of pi(n)

Example

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

Mathematica

Table[Mod[PrimePi[10^n], 2], {n, 0, 10}] (* T. D. Noe, Nov 13 2012 *)

Prog

(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;
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

Crossrefs

Cf. A006880, A219097, A219098.

Sequence in context: A144606 A060510 A327205 * A072629 A164292 A337802

Adjacent sequences: A219068 A219069 A219070 * A219072 A219073 A219074

Keyword

nonn

Author

Henri Lifchitz, Nov 11 2012

Status

approved