(*start*)
(*Mathematica 8*)
nn = 1000;
Monitor[a1 =
  Table[(n + 1)*(Round[(Exp[1/(Im[ZetaZero[n + 1]]/(2*Pi))] - 1)^-1] -
       Round[(Exp[1/(Im[ZetaZero[n]]/(2*Pi))] - 1)^-1]), {n, 1,
    nn}], n]
a2 = DeleteCases[a1, 0]
b = Table[Sum[Round[Log[n]], {n, 1, k}], {k, 3, Length[a2] + 2}]
cc = a2 - b;
cc[[1 ;; 20]]
Label
g1 = ListLinePlot[a2, PlotStyle -> Red, PlotLabel -> "sequence a2"]
g2 = ListLinePlot[b, PlotLabel -> "asymptotic b"]
g3 = Show[g1, g2,
  PlotLabel -> "sequence a2 and asymptotic b superimposed"]
g4 = ListLinePlot[cc,
  PlotLabel -> "difference between sequence a2 and asymptotic b"]
GraphicsGrid[{{g1, g2}, {g3, g4}}]
(*end*)