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A219071 Parity of pi(10^n). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A289074 A289242 A188037 * A257531 A288622 A214090

Adjacent sequences:  A219068 A219069 A219070 * A219072 A219073 A219074

KEYWORD

nonn

AUTHOR

Henri Lifchitz, Nov 11 2012

STATUS

approved

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Last modified September 22 22:42 EDT 2018. Contains 315270 sequences. (Running on oeis4.)