Illustration for A060208

Illustration for A060208 sequence

ID Number: A060208
Sequence:

1,0,1,0,2,1,2,2,1,0,2,1,3,3,2,1,3,3,4,4,3,2,4,3,3,3,2,2,4,3, 4,4,4,3,3,2,3,3,3,2,4,3,5,5,4,4,6,6,5,5,4,3,5,4,3,3,2,2,4,4,
6,6,6,5,5,4,6,6,5,4,6,6,8,8,7,6,6,6,7,7,7,6,8,7,7,7,6,6,8,7,
6,6,6,6,6,5,6,6,5,4,6,6,8,8,8
Signed: -1,0,1,0,2,1,2,2,1,0,2,1,3,3,2,1,3,3,4,4,3,2,4,3,3,3,2,2,4,
3,4,4,4,3,3,2,3,3,3,2,4,3,5,5,4,4,6,6,5,5,4,3,5,4,3,3,2,2,4,
4,6,6,6,5,5,4,6,6,5,4,6,6,8,8,7,6,6,6,7,7,7,6,8,7,7,7,6,6,8,
7,6,6,6,6,6,5,6,6,5,4,6,6,8,8,8,7,9,9,11,11,11,10,12,11,10,
10,9,9,9,8,7,7
Name: Difference between 2Pi(n) and Pi(2n), where Pi is A000720; or residue of 2Pi(n) modulo
Pi(2n); n=1 is singular subscript.
Formula: a(n)=Mod[2*PrimePi[n],PrimePi[2n]]=2*A000720(n)-A000720(2n)
for n>1;for n=1 it is the difference.
Example: n=100, Pi(100)=25, Pi(200)=46, 2*Pi(100)-Pi(2*100) =4=a(100)
See also: A000720,A022457
Keywords: sign,done
Offset: 0
Author(s): Labos E. (labos@ana1.sote.hu), Mar 19 2001