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A167146 a(n) = Im(rz(n)) - Im(-log(exp(-rz(n)))))/Pi where rz(n) is the n-th zero of Zeta(s). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A087789 A071830 A276982 * A020891 A090967 A272475

Adjacent sequences:  A167143 A167144 A167145 * A167147 A167148 A167149

KEYWORD

nonn

AUTHOR

Stephen Crowley, Oct 28 2009

STATUS

approved

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Last modified June 25 22:16 EDT 2019. Contains 324358 sequences. (Running on oeis4.)