A082899 a(n) = A082893(n)-A000040(n), that is difference of n-th prime and number closest to it and divisible by n.

0, 1, 1, 1, -1, -1, -3, -3, 4, 1, 2, -1, -2, -1, -2, -5, -8, -7, 9, 9, -10, 9, 9, 7, 3, 3, 5, 5, 7, 7, -3, -3, -5, -3, -9, -7, -9, -11, -11, -13, -15, -13, -19, -17, -17, -15, -23, 17, 18, 21, 22, 21, 24, 19, 18, 17, 16, 19, 18, 19, 22, 17, 8, 9, 12, 13, 4, 3, -2, 1, 2, 1, -2, -3, -4, -3, -4, -7, -6, -9, -14, -11, -16, -13, -14, -13, -14

Offset: 1

Author

Labos Elemer, Apr 22 2003

Keywords

• sign

Comments

n=9:p(9)=23 is between 18 and 27, closer to 27, so a(9)=27-23=+4.

Crossrefs

Cf. A082893-A082901.

Programs

Mathematica

Table[Prime[n]-n*Floor[(Floor[n/2]+Prime[n])/n], {n, 1, 100}]

Formula

a(n)=p[n]-n*floor[(floor(n/2)+p[n])/n], where p[n] is the n-th prime.