OFFSET
0,2
COMMENTS
Because series Sum_{m>=1} 1/z(m) is divergent this sequence is infinite.
Sum_{m>=1} 1/z(m)^2 = 0.0231049931...; see A332645.
Sum_{m>=1} 1/(1/4 + z(m)^2) = 0.023095708966... see A074760.
Sum_{m>=1} 1/(1/2 + i*z(m))^2 + 1/(1/2 - i*z(m))^2 = -0.046154317... see A245275.
Sum_{m>=1} 1/(1/2 + i*z(m))^3 + 1/(1/2 - i*z(m))^3 = -0.00011115823... see A245276.
a(11)-a(39) computed by David Platt, Mar 20 2020.
LINKS
Artur Jasinski, Table of n, a(n) for n = 0..39
Kano Kono, Vieta's Formulas on Completed Riemann Zeta, Alien's Mathematics.
EXAMPLE
a(0)=1 because 1/z(1) = 0.070747749954285585596 > 0
a(1)=93 because Sum_{m=1..93} 1/z(m) = 1.00082895080028509266 > 1
a(2)=621 because Sum_{m=1..621} 1/z(m) = 2.00017203211984838994 > 2.
MATHEMATICA
aa = {}; kk = 0; b = 0; Do[b = b + N[1/Im[ZetaZero[n]], 30];
If[b > kk, AppendTo[aa, n]; kk = kk + 1]; , {n, 1, 1000000}]; aa
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Feb 17 2020
EXTENSIONS
More terms from Artur Jasinski, Feb 21 2020
STATUS
approved