A072080 Number of (nontrivial) zeros of zeta(z) with 0 < Im(z) < 10^n.

0, 29, 649, 10142, 138069, 1747146, 21136125, 248008025, 2846548032, 32130158315, 357948363084, 3945951430271, 43124192297102, 467888702914983, 5045354828589535, 54118226280292478

Offset

1,2

Comments

a(n) ~ A259506(10^n). - Arkadiusz Wesolowski, Nov 08 2015

Links

Table of n, a(n) for n=1..16.

LMFDB base, Zeros of zeta(s) (computed by David Platt).

Andrew Odlyzko, Tables of zeros of the Riemann zeta function

Mathematics StackExchange user Rudolph, Does this contour integral actually count the roots of zeta(s) with imaginary part <T?, 2018. [Gives a(17)-a(20) as 577829042746896155, 6144758226908675407, 65112260263483892774, 687769382578810314775.]

Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros

Eric Weisstein's World of Mathematics, Xi-Function

Index entries for zeta function.

Prog

(PARI) a(n)=#lfunzeros(lzeta, 10^n) \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Sequence in context: A199038 A182329 A329016 * A263515 A201245 A063044

Adjacent sequences: A072077 A072078 A072079 * A072081 A072082 A072083

Keyword

nonn,more

Author

Eric W. Weisstein, Jun 13 2002

Extensions

More terms from Andrew Odlyzko, Jun 14 2002

a(7)-a(11) based on LMFDB data from Artur Jasinski, Jan 03 2020

a(11) corrected based on LMFDB data by Charles R Greathouse IV, Aug 23 2022

a(12)-a(16) added by Fredrik Johansson, May 01 2023

Status

approved