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A327543 Indices n of Gram points g(n) for successive positive maxima of the Riemann zeta function on critical line.

%I A327543 #34 Oct 23 2019 15:56:10
%S A327543 1,2,4,7,13,24,32,63,78,125,182,255,378,566,704,794,963,1112,1486,
%T A327543 1544,1934,2566,3295,3471,3969,6397,6619,8373,8570,9178,10172,10941,
%U A327543 11566,12346,13297,13880,15322,25462,28118,36718,64414,70855,83453,100051,103714,146918,185012,220570
%N A327543 Indices n of Gram points g(n) for successive positive maxima of the Riemann zeta function on critical line.
%C A327543 Gram points occur when the imaginary part of Riemann zeta function is zero but the real part nonzero.
%C A327543 The n-th Gram point occurs when the Riemann-Siegel theta function is equal to Pi*n.
%C A327543 For indices of Gram points g(n) for successive positive minima of the Riemann zeta function on critical line see A326890.
%C A327543 For indices of Gram points g(n) for successive negative minima of the Riemann zeta function on critical line see A326891.
%C A327543 For indices of Gram points g(n) for successive negative maxima of the Riemann zeta function on critical line see A325932.
%e A327543    n | a(n) | Zeta(1/2 + I*g(a(n))) |    g(a(n))
%e A327543   ---+------+-----------------------+------------
%e A327543    1 |    1 |  1.45742704787401225  | 23.17028270
%e A327543    2 |    2 |  2.84509123805192195  | 27.67018222
%e A327543    3 |    4 |  2.93812153849374056  | 35.46718430
%e A327543    4 |    7 |  3.66290294911991710  | 45.59302898
%e A327543    5 |   13 |  4.16439875850106581  | 63.10186798
%e A327543    6 |   24 |  4.47536695704548069  | 90.75295338
%e A327543    7 |   32 |  5.18702282127077889  | 108.9364311
%e A327543    8 |   63 |  5.97089319007464658  | 171.8101081
%e A327543    9 |   78 |  6.06256772354879599  | 199.6489681
%e A327543   10 |  125 |  7.00315163729736922  | 280.8024294
%e A327543   11 |  182 |  7.56958843983997014  | 371.5556258
%e A327543   12 |  255 |  8.24960849238073236  | 480.4061559
%e A327543   13 |  378 |  9.14820901096157903  | 652.2447407
%e A327543   14 |  566 |  9.37745383604127446  | 897.7841913
%e A327543   15 |  704 |  9.81879930244819679  | 1069.412795
%e A327543   16 |  794 | 10.35506137680061993  | 1178.447136
%t A327543 ff = 0; aa = {}; Do[kk = Re[Zeta[1/2 + I N[InverseFunction[RiemannSiegelTheta][n Pi], 10]]]; If[kk > ff, AppendTo[aa, n]; ff = kk], {n, 1, 250000}]; aa
%Y A327543 Cf. A114856, A254297, A255739, A255742, A325932, A326502, A326890, A326891.
%K A327543 nonn
%O A327543 1,2
%A A327543 _Artur Jasinski_, Sep 16 2019