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A065434 Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.

%I A065434 #33 Dec 01 2024 10:54:10
%S A065434 2,1,0,2,2,0,3,9,6,3,8,7,7,1,5,5,4,9,9,2,6,2,8,4,7,9,5,9,3,8,9,6,9,0,
%T A065434 2,7,7,7,3,3,4,3,4,0,5,2,4,9,0,2,7,8,1,7,5,4,6,2,9,5,2,0,4,0,3,5,8,7,
%U A065434 5,9,8,5,8,6,0,6,8,8,9,0,7,9,9,7,1,3,6,5,8,5,1,4,1,8,0,1,5,1,4
%N A065434 Decimal expansion of imaginary part of 2nd nontrivial zero of Riemann zeta function.
%D A065434 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.15.3, p. 138.
%H A065434 Enrico Bombieri, <a href="http://www.claymath.org/sites/default/files/official_problem_description.pdf">Problems of the Millennium: the Riemann Hypothesis</a>, Clay Mathematics Institute.
%H A065434 Andrew M. Odlyzko, <a href="http://www.plouffe.fr/simon/constants/zeta100.html">The first 100 (non trivial) zeros of the Riemann Zeta function, to over 1000 decimal digits each</a>, AT&T Labs - Research.
%H A065434 Andrew M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/zeta_tables/index.html">Tables of zeros of the Riemann zeta function</a>
%H A065434 <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%e A065434 The zero is at 1/2 + i*21.0220396387715549926284795938969...
%p A065434 Digits:= 150; Re(fsolve(Zeta(1/2+I*t)=0, t=21)); # _Iaroslav V. Blagouchine_, Jun 25 2016
%t A065434 ZetaZero[2] // Im // RealDigits[#, 10, 99]& // First (* _Jean-François Alcover_, Mar 05 2013 *)
%o A065434 (PARI) solve(x=21,22,real(zeta(1/2+x*I))) \\ _Charles R Greathouse IV_, Jun 30 2011
%o A065434 (PARI) lfunzeros(1,[21,22])[1] \\ _M. F. Hasler_, Nov 23 2018
%Y A065434 Imaginary part of k-th nontrivial zero of Riemann zeta function: A058303 (k=1), A065434 (k=2: this), A065452 (k=3), A065453 (k=4), A192492 (k=5), A305741 (k=6), A305742 (k=7), A305743 (k=8), A305744 (k=9), A306004 (k=10).
%Y A065434 Cf. A002410 (round), A013629 (floor).
%K A065434 nonn,cons
%O A065434 2,1
%A A065434 _N. J. A. Sloane_, Nov 24 2001