Voozh

A079630

Numbers n such that |real(zeta(1/2 + n*I))| exceeds all previous values, where zeta is the Riemann zeta function.

0, 10, 17, 18, 28, 46, 63, 109, 172, 281, 417, 652, 698, 852, 1269, 1550, 3100, 4478, 6726, 7578, 9654, 9826, 10678, 14304, 30775, 45079, 57552, 74956, 105731, 248917, 289346, 340761, 407722, 440699, 457170, 682764, 795112, 849038, 874546, 1138384

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

If you begin at 1 instead of 0, the sequence begins 1,2,3,4,5,6,7,8,9,10,..., etc.

LINKS

Table of n, a(n) for n=1..40.

Glen Pugh, The Riemann Hypothesis in a Nutshell

Ed Pegg Jr., The Riemann Hypothesis

EXAMPLE

|real(zeta(1/2 + 1616584*I))| ~= 44.1381

MATHEMATICA

a = -1; Do[b = Abs[ Re[ N[ Zeta[0.5 + n*I]]]]; If[b > a, Print[n]; a = b], {n, 0, 10^6}]

DeleteDuplicates[Table[{n, Abs[Re[N[Zeta[1/2+n I]]]]}, {n, 0, 12*10^5}], GreaterEqual[ #1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Jul 29 2024 *)

CROSSREFS

Cf. A002410.

Sequence in context: A157159 A176664 A256346 * A175389 A350779 A280591

Adjacent sequences: A079627 A079628 A079629 * A079631 A079632 A079633

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jan 30 2003

STATUS

approved

URL: https://oeis.org/A079630

⇱ A079630 - OEIS