A300304 Decimal expansion of the solution to 2*(1-x)^x = x^x.

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

Offset: 0

Author

Hugo Pfoertner, Mar 02 2018

Keywords

• nonn
• cons

Examples

			0.7228920811831477955323653512197716743558777367686417201254365151991...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Seqfan Mailing List Thread, 2(x - 1)^x = x^x, with contributions from _Juri-Stepan Gerasimov_, _Robert G. Wilson v_, _Neil Fernandez_, _Simon Plouffe_, _Walter Kehowski_, _G. C. Greubel_.

Programs

Mathematica

RealDigits[1/(1 + LambertW[Log[2]/2]/Log[2]), 10, 100][[1]] (* G. C. Greubel, Mar 02 2018 *)

PARI

1/(1 + lambertw(log(2)/2)/log(2)) \\ G. C. Greubel, Mar 02 2018

Formula

x = 1 / (1 + W(log(2)/2)/log(2)), where W(x) is the Lambert W-function; from G. C. Greubel.