A304022 Decimal expansion of the solution to (1 - x)*(1 + x)^x = x^x.
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, 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, 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
Offset: 0
Examples
0.3912468084543427683481984816602405435...
Programs
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Mathematica
Take[RealDigits[x /. FindRoot[(1 - x)*(1 + x)^x == x^x, {x, 1/2}, WorkingPrecision -> 120], 10][[1]], 105] -
PARI
solve(x=1/3, 1, (1 - x)*(1 + x)^x - x^x) \\ Michel Marcus, May 04 2018
Extensions
More digits from Alois P. Heinz, May 04 2018