This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286707 #9 May 14 2017 00:13:03
%S A286707 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,1,1,1,1,2,2,
%T A286707 2,2,2,3,3,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,7,8,9,9,9,10,10,10,10,11,11,
%U A286707 11,12,13,13,13,13,13,14,14,15,15,16,16,16,17,17,17,18,18,19,19,20,20,20,21,21,22,22,22,23,24,24,24,24,25,25,26,27,27,27,28,28
%N A286707 a(n) = (RiemannSiegelTheta(n)+im(log(zeta(1/2+i*n))))/Pi.
%C A286707 a(n) is not the same as A135297(n) - 1.
%H A286707 André LeClair, <a href="https://www.classe.cornell.edu/~leclair/Riemann_Colloq.pdf">The Riemann Hypothesis for physicists, page 30</a>.
%H A286707 Raymond Manzoni, <a href="https://math.stackexchange.com/a/442686/8530">Mathematics Stack Exchange: Riemann Zeta function - number of zeros</a>.
%F A286707 a(n) = im(LogGamma (1/4 + I*n/2))/Pi - n/(2*Pi)*log (Pi) + im(log(zeta(1/2 + I*n)))/Pi
%F A286707 a(n) = floor(im(LogGamma (1/4 + I*n/2))/Pi - n/(2*Pi)*log(Pi) + 1) + (sign(im(zeta (1/2 + I*n))) - 1)/2
%F A286707 a(n) = (RiemannSiegelTheta(n) + im(log (zeta (1/2 + I*n))))/Pi
%F A286707 a(n) = (floor(RiemannSiegelTheta(n)/Pi + 1)) + (sign(im (zeta(1/2 + I*n))) - 1)/2
%F A286707 a(n) = n/(2*Pi)*log[n/(2*Pi*Exp(1))] + 7/8 + (im(log (zeta (1/2 + I*n))))/Pi - 1 - BigO(n^(-1))
%F A286707 a(n) = floor(n/(2*Pi)*log(n/(2*Pi*exp(1))) + 7/8) + (sign(im(zeta (1/2 + I*n))) - 1)/2
%t A286707 a = Table[Round[((Im[LogGamma[1/4 + I*t/2]]/Pi - t/(2*Pi)*Log[Pi] + Im[Log[Zeta[1/2 + I*t]]]/Pi))], {t, 1, 100}]
%t A286707 a = Table[Round[((Floor[Im[LogGamma[1/4 + I*t/2]]/Pi - t/(2*Pi)*Log[Pi] + 1] + (Sign[Im[Zeta[1/2 + I*t]]] - 1)/2))], {t, 1, 100}]
%t A286707 a = Table[Round[((RiemannSiegelTheta[t] + Im[Log[Zeta[1/2 + I*t]]])/Pi)], {t, 1, 100}]
%t A286707 a = Table[Round[((Floor[RiemannSiegelTheta[t]/Pi + 1]) + (Sign[Im[Zeta[1/2 + I*t]]] - 1)/2)], {t, 1, 100}]
%t A286707 a = Table[Round[(Floor[t/(2*Pi)*Log[t/(2*Pi*Exp[1])] + 7/8] + (Sign[Im[Zeta[1/2 + I*t]]] - 1)/2)], {t, 1, 100}]
%t A286707 a = Table[Round[(t/(2*Pi)*Log[t/(2*Pi*Exp[1])] + 7/8 + (Im[Log[Zeta[1/2 + I*t]]])/Pi - 1)], {t, 1, 100}]
%Y A286707 Cf. A135297.
%K A286707 sign
%O A286707 1,26
%A A286707 _Mats Granvik_, May 13 2017