%I #12 May 05 2018 05:15:52

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

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

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

%N Decimal expansion of the solution to (1 - x)*(1 + x)^x = x^x.

%e 0.3912468084543427683481984816602405435...

%t Take[RealDigits[x /. FindRoot[(1 - x)*(1 + x)^x == x^x, {x, 1/2}, WorkingPrecision -> 120], 10][[1]], 105]

%o (PARI) solve(x=1/3, 1, (1 - x)*(1 + x)^x - x^x) \\ _Michel Marcus_, May 04 2018

%Y Cf. A302973, A303069.

%K nonn,cons

%O 0,1

%A _Juri-Stepan Gerasimov_, May 04 2018

%E More digits from _Alois P. Heinz_, May 04 2018