A167146 a(n) = (Im(rz(n)) - Im(-log(exp(-rz(n)))))/Pi where rz(n) is the n-th zero of Zeta(s).

4, 6, 8, 10, 10, 12, 14, 14, 16, 16, 16, 18, 18, 20, 20, 22, 22, 22, 24, 24, 26, 26, 26, 28, 28, 30, 30, 30, 32, 32, 34, 34, 34, 36, 36, 36, 36, 38, 38, 40, 40, 40, 42, 42, 42, 42, 44, 44, 44, 46, 46, 46, 48, 48, 48, 50, 50, 50, 52, 52, 52, 54, 54, 54, 56, 56, 56, 56, 58, 58

Offset

1,1

Comments

I strongly suspect that lim_{n -> infinity} a(n)/n = 3/4. - Stephen Crowley, Oct 28 2009

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

From Mats Granvik, Jan 15 2018: (Start)

a(n) = (Im(zetazero(n)) - Im(-log(exp(-1/2 - i*Im(zetazero(n))))))/Pi, where i = sqrt(-1).

a(n) = 2*A275579(n) = 2*round(Im(zetazero(n))/(2*Pi)), verified for n=1..100000.

a(n) = (Im(zetazero(n)) - arctan(cos(Im(zetazero(n))), sin(Im(zetazero(n)))))/Pi, verified for n=1..100000.

(End)

Maple

[seq(round(evalf((Im(rzerof(n))-Im(-ln(exp(-rzerof(n)))))/Pi)), n = 1 .. 100)] # where rzerof(n) is the n-th zero of the Riemann zeta function, the rounding is simply for presentation purposes, the values are actually integers

Mathematica

Table[2*Round[Im[ZetaZero[n]]/(2*Pi)], {n, 1, 70}] (* Mats Granvik, Jan 15 2018 *)

Crossrefs

Cf. A002410, A275579.

Sequence in context: A071830 A276982 A340846 * A020891 A340848 A090967

Adjacent sequences: A167143 A167144 A167145 * A167147 A167148 A167149

Keyword

nonn

Author

Stephen Crowley, Oct 28 2009

Status

approved