

A082668


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


1



14, 50, 237, 1419, 9878, 74921, 600270, 4992381, 42653550, 371870204, 3293531632, 29538618432, 267653395649, 2445999556030, 22514484222486, 208514052006405, 1941393531395155, 18159447720050928
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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: A225921 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



