|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|