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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

Table of n, a(n) for n=1..48.

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.)