A275579 Nearest integer to imaginary part of Riemann zeta zeros divided by 2*Pi.

2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26

Offset

1,1

Comments

This sequence never increases by more than 1. The first differences are given by A275737 starting: 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, ...

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Guilherme França, André LeClair, Statistical and other properties of Riemann zeros based on an explicit equation for the n-th zero on the critical line, arXiv:1307.8395 [math.NT], 2013-2014, page 13, formula (25).

Formula

a(n) = round(im(zetazero(n))/(2*Pi)) = round(A002410(n)/(2*Pi)).

a(n) ~ (n - 11/8)/LambertW(exp(1)^(-1)*(n - 11/8)) (This is the Franca LeClair asymptotic at page 13, formula (25).)

Mathematica

Table[Round[Im[ZetaZero[n]]/(2*Pi)], {n, 1, 60}]

Crossrefs

Cf. A199499, A046654, A275341, A275737.

Sequence in context: A064067 A202306 A373178 * A198292 A020892 A196165

Adjacent sequences: A275576 A275577 A275578 * A275580 A275581 A275582

Keyword

nonn

Author

Mats Granvik, Aug 02 2016

Status

approved