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%I #21 May 05 2020 10:03:50
%S 2,9,5,9,0,5,0,0,5,5,7,5,2,1,3,9,5,5,6,4,7,2,3,7,8,3,1,0,8,3,0,4,8,0,
%T 3,3,9,4,8,6,7,4,1,6,6,0,5,1,9,4,7,8,2,8,9,9,4,7,9,9,4,3,4,6,4,7,4,4,
%U 3,5,8,2,0,7,2,4,5,1,8,7,7,9,2,1,6,8,7,1,4,3,6,0,2,1,7,1,5
%N Decimal expansion of -C, where C = -0.2959050055752... is the real solution < 0 to zeta(x) = x.
%C Start from any complex number z=x+iy, not solution to zeta(z)=z, iterate the zeta function on z. If zeta_m(z)=zeta(zeta(....(z)..)) m times, has a limit when m grows, then this limit seems to always be the real number C = -0.2959050055752....
%C C is not only a real fixed point of zeta, but the only attractive fixed point of Riemann zeta on the real line. - _Balarka Sen_, Feb 21 2013
%H Balarka Sen, <a href="/A069857/b069857.txt">Table of n, a(n) for n = 0..200</a>
%e Let z=3+5I after 30 iterations : zeta_30(z)=-0.29590556499...-0.00000041029065...*I
%t FindRoot[Zeta[z] - z, {z, 0}, WorkingPrecision -> 500] (* _Balarka Sen_, Feb 21 2013 *)
%o (PARI) -solve(x=-1, 0, zeta(x)-x) \\ _Michel Marcus_, May 05 2020
%K cons,easy,nonn
%O 0,1
%A _Benoit Cloitre_, Apr 27 2002
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