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