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 A327543 Indices n of Gram points g(n) for successive positive maxima of the Riemann zeta function on critical line. 4
 1, 2, 4, 7, 13, 24, 32, 63, 78, 125, 182, 255, 378, 566, 704, 794, 963, 1112, 1486, 1544, 1934, 2566, 3295, 3471, 3969, 6397, 6619, 8373, 8570, 9178, 10172, 10941, 11566, 12346, 13297, 13880, 15322, 25462, 28118, 36718, 64414, 70855, 83453, 100051, 103714, 146918, 185012, 220570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Gram points occur when the imaginary part of Riemann zeta function is zero but the real part nonzero. The n-th Gram point occurs when the Riemann-Siegel theta function is equal to Pi*n. For indices of Gram points g(n) for successive positive minima of the Riemann zeta function on critical line see A326890. For indices of Gram points g(n) for successive negative minima of the Riemann zeta function on critical line see A326891. For indices of Gram points g(n) for successive negative maxima of the Riemann zeta function on critical line see A325932. LINKS EXAMPLE n | a(n) | Zeta(1/2 + I*g(a(n))) |    g(a(n))   ---+------+-----------------------+------------    1 |    1 |  1.45742704787401225  | 23.17028270    2 |    2 |  2.84509123805192195  | 27.67018222    3 |    4 |  2.93812153849374056  | 35.46718430    4 |    7 |  3.66290294911991710  | 45.59302898    5 |   13 |  4.16439875850106581  | 63.10186798    6 |   24 |  4.47536695704548069  | 90.75295338    7 |   32 |  5.18702282127077889  | 108.9364311    8 |   63 |  5.97089319007464658  | 171.8101081    9 |   78 |  6.06256772354879599  | 199.6489681   10 |  125 |  7.00315163729736922  | 280.8024294   11 |  182 |  7.56958843983997014  | 371.5556258   12 |  255 |  8.24960849238073236  | 480.4061559   13 |  378 |  9.14820901096157903  | 652.2447407   14 |  566 |  9.37745383604127446  | 897.7841913   15 |  704 |  9.81879930244819679  | 1069.412795   16 |  794 | 10.35506137680061993  | 1178.447136 MATHEMATICA 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 CROSSREFS Cf. A114856, A254297, A255739, A255742, A325932, A326502, A326890, A326891. Sequence in context: A018182 A005595 A296689 * A096236 A002574 A069765 Adjacent sequences:  A327540 A327541 A327542 * A327544 A327545 A327546 KEYWORD nonn AUTHOR Artur Jasinski, Sep 16 2019 STATUS approved

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Last modified December 1 05:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)