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