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%I #24 Nov 25 2017 04:27:28
%S 7,0,3,5,0,6,0,7,6,4,3,0,6,6,2,4,3,0,9,6,9,2,9,6,6,1,6,2,1,7,7,7,0,9,
%T 5,2,1,3,2,4,6,8,4,5,7,4,2,4,2,8,1,5,5,5,5,8,6,2,1,5,7,1,6,5,1,0,5,1,
%U 2,3,0,6,0,0,3,9,9,4,0,1,4,4,9,5,2,5,4,5,6,8,0,4,6,0,5,7,3,1,5,1,9,8,5,4,4,8,3
%N Decimal expansion of the root of the equation (1-r)^(2*r-1) = r^(2*r).
%C Constant is associated with A167008, A219206 and A219207.
%e 0.70350607643066243...
%p Digits:= 140:
%p v:= convert(fsolve( (1-r)^(2*r-1) = r^(2*r), r=1/2), string):
%p seq(parse(v[n+2]), n=0..120); # _Alois P. Heinz_, Dec 12 2012
%t RealDigits[r/.FindRoot[(1-r)^(2*r-1)==r^(2*r),{r,1/2}, WorkingPrecision->250], 10, 200][[1]]
%o (PARI) solve(x=.7,1,(1-x)^(2*x-1) - x^(2*x)) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y Cf. A167008, A219206, A219207, A228808, A184731, A206154, A206156, A206158, A237421, A295611.
%K nonn,cons
%O 0,1
%A _Vaclav Kotesovec_, Dec 12 2012
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