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A082668 (10^n)-th zero of the Riemann zeta function rounded to the nearest integer.

%I A082668 #32 Feb 16 2025 08:32:49
%S A082668 14,50,237,1419,9878,74921,600270,4992381,42653550,371870204,
%T A082668 3293531632,29538618432,267653395649,2445999556030,22514484222486,
%U A082668 208514052006405,1941393531395155,18159447720050928
%N A082668 (10^n)-th zero of the Riemann zeta function rounded to the nearest integer.
%C A082668 a(21) = 144176897509546973538, a(22) = 1370919909931995308227 and a(23) = 13066434408793494969602.
%D A082668 John Derbyshire, Prime Obsession, Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Joseph Henry Press, Washington, D.C., 2003.
%D A082668 Karl Sabbagh, The Riemann Hypothesis, The Greatest Unsolved Problem In Mathematics, Farrar, Straus and Giroux, NY, 2002.
%H A082668 A. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables/">Tables of zeros of the Riemann zeta function</a>
%H A082668 Glen Pugh, <a href="https://web.archive.org/web/20051215154301/http://www.math.ubc.ca:80/~pugh/RiemannZetaComplex/">Zeta Function Plotter</a>
%H A082668 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannZetaFunctionZeros.html">Riemann Zeta Function Zeros</a>
%H A082668 <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%F A082668 a(n) = A002410(10^n). - _Ryan Propper_, Feb 12 2008
%t A082668 Table[Round[N[Im[ZetaZero[10^i]], 17]], {i, 0, 7}] (* _David Baugh_, Nov 03 2011 *)
%Y A082668 Cf. A072080, A002410, A072080.
%K A082668 nonn
%O A082668 0,1
%A A082668 _Robert G. Wilson v_, May 18 2003
%E A082668 600270 (taken from Odlyzko's tables) from _Ryan Propper_, Feb 12 2008
%E A082668 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