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A326891 Successive negative minima of Gram's points g(n) of the Riemann zeta function.

%I A326891 #24 Apr 16 2022 15:04:00
%S A326891 126,134,777,1165,2808,3782,12174,14374,23149,60780,117807,126085
%N A326891 Successive negative minima of Gram's points g(n) of the Riemann zeta function.
%C A326891 This sequence is subset of A114856.
%C A326891 Gram's points occur when the imaginary part of Riemann zeta function is zero but the real part isn't zero.
%C A326891 For very small values of Gram's points, the distance between nearest zero of Riemann zeta function is very small.
%C A326891 For successive positive minima of Gram's points g(n) of the Riemann zeta function see A326890.
%H A326891 M. A. Korolev, <a href="https://doi.org/10.4213/sm8253">On small values of the Riemann zeta-function at Gram points</a>, Mat. Sb., 2014, Volume 205, Number 1, 67-86. In Russian.
%e A326891    n |  a(n)  | g(a(n)) = Zeta value
%e A326891   ---+--------+---------------------
%e A326891    1 |    126 | -0.02762949885719994
%e A326891    2 |    134 | -0.01690039090339079
%e A326891    3 |    777 | -0.00964626429746985
%e A326891    4 |   1165 | -0.008575843736423
%e A326891    5 |   2808 | -0.005747300941326
%e A326891    6 |   3782 | -0.000760294730822
%e A326891    7 |  12174 | -0.00045763304501
%e A326891    8 |  14374 | -0.00027891005688
%e A326891    9 |  23149 | -0.00007068683846
%e A326891   10 |  60780 | -0.0000398945276
%e A326891   11 | 117807 | -0.0000229487717
%e A326891   12 | 126085 | -0.0000077126884
%t A326891 ee = 10; cc = {}; Do[kk = Re[Zeta[1/2 + I N[InverseFunction[ RiemannSiegelTheta][n Pi], 10]]];If[(kk < 0) && (Abs[kk] < ee), AppendTo[cc, n]; ee = Abs[kk]], {n, 1, 1000000}]; aa
%Y A326891 Cf. A114856, A326890.
%K A326891 nonn,more
%O A326891 1,1
%A A326891 _Artur Jasinski_, Sep 13 2019