A126583 Decimal expansion of solution to exp(-x) = x^2.

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

Offset: 0

Author

Denton J. Dailey (djd1497(AT)aol.com), Jan 05 2007

Keywords

• cons
• nonn

Comments

The value of the infinite power tower function x^x^x... at x = sqrt(1/e). - Alois P. Heinz, Oct 19 2016

Examples

			0.7034674224983916520498186018599021303429284310342236...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Tetration
• Index entries for transcendental numbers

Crossrefs

Cf. A030178, A099554, A202356.

Programs

Mathematica

RealDigits[ FindRoot[ Exp[ -x] == x^2, {x, {.5, 1}}, WorkingPrecision -> 120][[1, 2, 1]], 10, 111][[1]]
RealDigits[ 2*ProductLog[1/2], 10, 102] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

2*lambertw(1/2) \\ G. C. Greubel, Mar 06 2018

Formula

Equals 2*LambertW(1/2). - Alois P. Heinz, Oct 19 2016

Equals log(A099554) = 2*A202356. - Hugo Pfoertner, Jul 19 2024