%I
%S 2,5,5,7,6,6,3,9,3,2,7,8,9,0,1,9,4,3,4,2,2,1,4,4,0,6,0,0,4,9,9,3,5,5,
%T 0,2,0,3,5,2,2,9,0,8,3,1,9,9,9,0,4,2,6,4,8,2,4,2,5,6,2,1,7,4,1,8,6,0,
%U 3,5,8,5,1,7,7,9,7,2,2,0,5,7,3,8,4,9,7,2,9,0,8,1,1,2,8,0,1,1,6,5,0,0,4,6,7,1
%N Decimal expansion of the position of the local minimum of the Barnes G function in the interval [2,4].
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BarnesGFunction.html">Barnes GFunction</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_Gfunction">Barnes Gfunction</a>
%F 3  2*x + log(2*Pi) + 2*(x1)*psi(x1) = 0, with 2<x<4, psi being the digamma function.
%e 2.557663932789019434221440600499355020352290831999042648242562174186...
%t digits = 105; x2 = x /. FindRoot[3  2*x + Log[2*Pi] + 2*(x1)*PolyGamma[x1] == 0, {x, 3}, WorkingPrecision > digits+10]; RealDigits[x2, 10, digits] // First
%Y Cf. A245081, A245082, A245084.
%K nonn,cons,easy
%O 1,1
%A _JeanFrançois Alcover_, Jul 11 2014
