login
Decimal expansion of the root of the equation (1-r)^(2*r) = r^(2*r+1).
9

%I #14 Nov 30 2014 14:25:19

%S 6,0,3,2,3,2,6,8,3,7,7,4,1,3,6,2,0,6,2,2,0,1,9,2,6,5,0,9,4,8,6,6,8,2,

%T 2,0,4,2,0,9,6,2,5,1,4,2,1,1,7,4,8,7,4,8,0,4,2,4,0,3,6,1,5,4,8,8,9,6,

%U 6,5,7,3,0,6,0,4,3,0,0,6,9,7,3,8,3,0,3,2,1,9,2,7,2,3,5,2,6,2,5,4,7,6,9,7,7,3

%N Decimal expansion of the root of the equation (1-r)^(2*r) = r^(2*r+1).

%H Vaclav Kotesovec, <a href="/A237421/b237421.txt">Table of n, a(n) for n = 0..105</a>

%e 0.6032326837741362...

%p Digits:= 140:

%p v:= convert(fsolve((1-r)^(2*r) = r^(2*r+1), r=1/2), string):

%p seq(parse(v[n+2]), n=0..120);

%t RealDigits[r/.FindRoot[(1-r)^(2*r)==r^(2*r+1), {r, 1/2}, WorkingPrecision->250], 10, 200][[1]]

%Y Cf. A206152, A227403, A220359.

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, Mar 04 2014