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A327546 Indices n of j-points j(n) for successive positive maxima of the Riemann zeta function on critical line.

%I A327546 #21 Oct 23 2019 15:56:49
%S A327546 1,3,6,12,23,31,39,62,124,181,211,254,377,703,869,1207,1443,1702,1933,
%T A327546 2565,3968,4657,4803,5815,6618,8569,13879,15321,25461,44681,58716,
%U A327546 62728,68865,74399,83452,100050,167369,181802,185011,220569,259499
%N A327546 Indices n of j-points j(n) for successive positive maxima of the Riemann zeta function on critical line.
%C A327546 j-points occur when the real part of Riemann zeta function is zero but the imaginary part isn't zero.
%C A327546 The n-th j-point occur when Riemann-Siegel theta function is equal to Pi*(2n+1)/2.
%e A327546    n |  a(n)  | Zeta[1/2+I*j(a(n))]  |  j(a(n))
%e A327546 -----+--------+----------------------+------------
%e A327546    1 |      1 | 0.6888099353665862*i |  25.49150821
%e A327546    2 |      3 | 1.0716782759460156*i |  33.62379307
%e A327546    3 |      6 | 1.3843203337013829*i |  43.99352729
%e A327546    4 |     12 | 2.0558319047400831*i |  61.73354345
%e A327546    5 |     23 | 2.2103659566253039*i |  89.57355850
%e A327546    6 |     31 | 2.4259114706957412*i |  107.8332676
%e A327546    7 |     39 | 2.5797839609135738*i |  125.0556067
%e A327546    8 |     62 | 3.5676523298409918*i |  170.8597635
%e A327546    9 |    124 | 3.9817183542258544*i |  279.9753243
%e A327546   10 |    181 | 4.4992991376133266*i |  370.7853980
%e A327546   11 |    211 | 4.7024313606767908*i |  416.3507516
%e A327546   12 |    254 | 4.9763959256849833*i |  479.6816189
%e A327546   13 |    377 | 6.0255895622763492*i |  651.5679685
%e A327546   14 |    703 | 6.6869029304615494*i | 1068.801198
%e A327546   15 |    869 | 6.9619624520146889*i | 1268.439833
%e A327546   16 |   1207 | 7.0560068592571360*i | 1658.281364
%t A327546 ff = 0; aa = {}; Do[kk = Im[Zeta[1/2 + I N[InverseFunction[RiemannSiegelTheta][(2 n + 1) Pi/2],10]]]; If[kk > ff, AppendTo[aa, n]; ff = kk], {n, 1, 100051}]; aa
%Y A327546 Cf. A114856, A254297, A255739, A255742, A325932, A326502, A326890, A326891, A327543.
%K A327546 nonn,more
%O A327546 1,2
%A A327546 _Artur Jasinski_, Sep 16 2019