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%I #21 Nov 16 2017 02:43:22
%S 3,2,3,8,0,5,1,1,8,9,4,5,9,5,7,4,2,9,8,2,3,6,0,0,9,8,0,9,8,7,9,7,7,2,
%T 9,0,6,0,4,5,1,0,3,3,6,0,4,8,2,5,3,8,5,5,4,1,4,2,0,3,5,9,9,4,7,0,9,8,
%U 5,0,0,7,6,9,2,5,8,3,8,0,5,2,5,7,9,5,2,2,5,8,5,8,4,1,9,7,4,6,6,1,3,8,4,3,2
%N Decimal expansion of the maximum value reached by the function -2*x*log(x)-2*x*(1-x) in the interval (0,1].
%C Equals 2(c-c^2) where c = A106533 (the rumor constant).
%H G. C. Greubel, <a href="/A226469/b226469.txt">Table of n, a(n) for n = 0..5000</a>
%e 0.3238051189459574298236009809879772906045103360482538554...
%t EE = -1/2 ProductLog[-2/(E^2)]; RealDigits[N[2*(EE-EE^2),100]][[1]]
%o (PARI) {a = solve(x=0.1, x=0.5, 2*log(x) - 4*x + 4)}; -2*a*log(a)-2*a*(1-a) \\ _G. C. Greubel_, Nov 16 2017
%Y Cf. A106533.
%K nonn,cons
%O 0,1
%A _José María Grau Ribas_, Jun 08 2013
%E Offset corrected by _Rick L. Shepherd_, Jan 02 2014
%E More terms from _Alois P. Heinz_, Jan 11 2014
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