A259506 a(n) = floor((LogGamma(n/2+1) - n*log(Pi)/2)/Pi).

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

Offset: 0

Author

Arkadiusz Wesolowski, Nov 08 2015

Keywords

• sign

Comments

Let f(n) = number of (nontrivial) zeros of zeta(z) with 0 < Im(z) < n; then f(n) ~ a(n).

The sequence gives exactly the values of A072080(n) for n = 2, 3, and 5.

Links

• Index entries for zeta function

Crossrefs

Cf. A002410, A072080, A082668, A254297.

Programs

Mathematica

Table[Floor[(LogGamma[n/2 + 1] - n*Log[Pi]/2)/Pi], {n, 0, 74}]

PARI

a(n)=floor((lngamma(n/2+1)-n*log(Pi)/2)/Pi)

Formula

a(n) = floor((LogGamma(n/2+1) - n*log(Pi)/2)/Pi).