A082668 - OEIS

A082668

(10^n)-th zero of the Riemann zeta function rounded to the nearest integer.

14, 50, 237, 1419, 9878, 74921, 600270, 4992381, 42653550, 371870204, 3293531632, 29538618432, 267653395649, 2445999556030, 22514484222486, 208514052006405, 1941393531395155, 18159447720050928

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

OFFSET

0,1

COMMENTS

a(21) = 144176897509546973538, a(22) = 1370919909931995308227 and a(23) = 13066434408793494969602.

REFERENCES

John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Joseph Henry Press, Washington, D.C., 2003.

Karl Sabbagh, The Riemann Hypothesis, The Greatest Unsolved Problem In Mathematics, Farrar, Straus and Giroux, NY, 2002.

LINKS

Table of n, a(n) for n=0..17.

A. Odlyzko, Tables of zeros of the Riemann zeta function

Glen Pugh, Zeta Function Plotter

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

Index entries for zeta function.

FORMULA

a(n) = A002410(10^n). - Ryan Propper, Feb 12 2008

MATHEMATICA

Table[Round[N[Im[ZetaZero[10^i]], 17]], {i, 0, 7}] (* David Baugh, Nov 03 2011 *)

CROSSREFS

Cf. A072080, A002410, A072080.

Sequence in context: A350850 A205354 A281699 * A231044 A231076 A158519

Adjacent sequences: A082665 A082666 A082667 * A082669 A082670 A082671

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, May 18 2003

EXTENSIONS

600270 (taken from Odlyzko's tables) from Ryan Propper, Feb 12 2008

a(2) corrected and a(7) through a(17) found by David Baugh using Mathematica and a theorem of (Littlewood, Turing, Lehman, Brent), a(22) corrected and a(23) added based on tables from Odlyzko, Nov 03 2011

STATUS

approved