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 A282897 #58 Jul 24 2017 11:44:04
%S A282897 1,3,5,8,10,11,14,16,17,18,20,21,23,25,28,29,32,33,35,36,37,40,41,44,
%T A282897 46,49,50,52,54,55,58,59,60,64,67,68,69,72,73,74,76,78,79,83,88,89,92,
%U A282897 94,98,99,103,104,105,108,109,110
%N A282897 Indices n such that sign(Im(zetazero(n)) - 2*Pi*e*exp(LambertW((n - 11/8)/e))) = -1.
%C A282897 The beginning of a(n) agrees with the sequence of numbers n such that floor(Im(zetazero(n))/(2*Pi)*log(Im(zetazero(n))/(2*Pi*e)) + 11/8 - n + 1) = 0, but disagrees later. The first disagreements are at n = 39326, 44469, 64258, 68867, 74401, 90053, 94352, 96239, ... and these numbers are in a(n) but not in the sequence that uses the floor function.
%C A282897 The beginning of a(n) also agrees with numbers n such that sign(Im(zeta(1/2 + i*2*Pi*e*exp(LambertW((n - 11/8)/e))))) = 1, but disagrees later. The first numbers that are in a(n) but not in the sequence that uses the sign function are n = 39325, 44468, ... The first numbers that are in the sequence that uses the sign function but not in a(n) are n = 28814, 30265, 36721, 45926, 46591, ... Compare this to the sequences in Remark 2 in A282896.
%C A282897 From _Mats Granvik_, Jun 17 2017: (Start)
%C A282897 There is at least an initial agreement between a(n) and the positions of zeros in: floor(2*(RiemannSiegelTheta(Im(ZetaZero(n)))/Pi - floor(RiemannSiegelTheta(Im(ZetaZero(n)))/Pi))). - _Mats Granvik_, Jun 17 2017
%C A282897 There is at least an initial agreement between a(n) and the positions of -1 in the sequence computed without prior knowledge of the exact locations of the Riemann zeta zeros, that instead uses the Franca-Leclair asymptotic as the argument to the zeta zero counting function. See the Mathematica program below.
%C A282897 Complement to A282896.
%C A282897 (End)
%H A282897 G. C. Greubel, <a href="/A282897/b282897.txt">Table of n, a(n) for n = 1..5400</a>
%H A282897 Mats Granvik, <a href="/A282897/a282897.txt">Mathematica programs to compute the sequence</a>
%F A282897 a(n) = positions where A288640 = 0.
%t A282897 FrancaLeClair[n_] = 2*Pi*Exp[1]*Exp[ProductLog[(n - 11/8)/Exp[1]]]; f = Table[Sign[Im[ZetaZero[n]] - FrancaLeClair[n]], {n, 1, 110}]; Flatten[Position[f, -1]]
%Y A282897 Cf. A002505, A135297, A153815, A273061, A282793, A282794, A282896, A282897.
%K A282897 nonn
%O A282897 1,2
%A A282897 _Mats Granvik_, Feb 24 2017