A290531 Second differences of argument(Zeta(1/2 + n*I))/Pi.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 1, -1, 1, -1, 1, -1, 0, 1, -1, 0, 1, -1, 1, -1, 1, -1, 0, 1, -1, 1, -1, 0, 1, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 1, -1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 2, -2, 0, 1, -1, 1, -1, 1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1

Offset

1,110

Comments

The result is rounded to the nearest integer. Values are very close to integers, almost exactly where the nontrivial zeros of the Zeta function occur.

Links

Table of n, a(n) for n=1..127.

Simon Plouffe, On the values of the zeta and gamma function, arXiv:1310.7195 [math.NT], 2013.

Mathematica

Table[Arg[Zeta[1/2 + n I]]/Pi, {n, 1, 129}] // Differences[#, 2]& // Round (* Jean-François Alcover, Feb 14 2019 *)

Crossrefs

Sequence in context: A089385 A124407 A294624 * A206442 A137581 A156311

Adjacent sequences: A290528 A290529 A290530 * A290532 A290533 A290534

Keyword

sign

Author

Simon Plouffe, Sep 03 2017

Status

approved