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A329751 Indices n of j-points j(n) for successive positive minima of the Riemann zeta function on critical line.

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%I A329751 #7 Jan 02 2020 20:49:50
%S A329751 1,9,14,27,38,288,28171,42680
%N A329751 Indices n of j-points j(n) for successive positive minima of the Riemann zeta function on critical line.
%C A329751 j-points occur when the real part of Riemann zeta function is zero but the imaginary part isn't zero.
%C A329751 The n-th j-point occur when Riemann-Siegel theta function is equal to Pi*(2n+1)/2.
%e A329751    n |  a(n)  |   j(a(n))      | zeta(1/2+i*j(a(n)))
%e A329751   ---+--------+----------------+----------------------
%e A329751    1 |      1 |    25.49150821 | 0.68880994 * i
%e A329751    2 |      9 |    53.21405637 | 0.59984107 * i
%e A329751    3 |     14 |    67.13274840 | 0.09483571 * i
%e A329751    4 |     27 |    98.85689819 | 0.09031281 * i
%e A329751    5 |     38 |   122.94885747 | 0.00316160 * i
%e A329751    6 |    288 |   528.40629391 | 0.00013121 * i
%e A329751    7 |  28171 | 24370.31450783 | 0.00004727 * i
%e A329751    8 |  42680 | 35149.21796047 | 0.00000366 * i
%t A329751 prec=20;ff = 10; aa = {}; Do[kk = Im[Zeta[1/2 + I N[InverseFunction[RiemannSiegelTheta][(2 n + 1) Pi/2], prec]]]; If[(kk < ff) && (kk > 0), AppendTo[aa, n]; ff = kk], {n,  1, 50000}]; aa
%Y A329751 Cf. A114856, A254297, A255739, A255742, A325932, A326502, A326890, A326891, A327543, A327546.
%K A329751 nonn,more
%O A329751 1,2
%A A329751 _Artur Jasinski_, Nov 20 2019