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

Offset: 0

Author

Robert G. Wilson v, May 18 2003

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A072080, A002410, A072080.

Programs

Mathematica

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

Formula

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

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