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%I #7 Apr 24 2016 03:26:24
%S 2,7,1,7,2,6,2,8,2,9,2,0,4,5,7,4,1,0,1,5,7,0,5,8,0,6,6,1,6,7,6,5,2,8,
%T 4,1,2,4,2,4,7,5,1,8,5,3,9,1,7,4,9,2,6,5,5,9,4,4,0,7,2,7,5,9,7,2,9,0,
%U 3,9,8,3,2,6,1,3,9,3,0,8,7,8,2,7,6,7,1,2,1,1,4,4,2,6,1,6,8,9,1,9,8,4,5,3,6
%N Decimal expansion of -x_1 such that the Riemann function zeta(x) has at real x_1<0 its first local extremum.
%C For real x < 0, zeta(x) undergoes divergent oscillations, passing through zero at every even integer value of x. In each interval (-2n,-2n-2), n = 1, 2, 3, ..., it attains a local extreme (maximum, minimum, maximum, ...). The location x_n of the n-th local extreme does not match the odd integer -2n-1. Rather, x_n > -2n-1 for n = 1 and 2, and x_n < -2n-1 for n >= 3. This entry defines the location x_1 of the first maximum. The corresponding value is in A271856.
%H Stanislav Sykora, <a href="/A271855/b271855.txt">Table of n, a(n) for n = 1..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%e x_1 = -2.7172628292045741015705806616765284124247518539174926559440...
%e zeta(x_1) = A271856.
%o (PARI) \\ This function was tested up to n = 11600000:
%o zetaextreme(n) = {return(solve(x=-2.0*n,-2.0*n-1.9999999999,zeta'(x));}
%o a = -zetaextreme(1) \\ Evaluation for this entry
%Y Cf. A271856.
%K nonn,cons
%O 1,1
%A _Stanislav Sykora_, Apr 23 2016
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