A175999 Decimal expansion of the definite integral of x^(1/x) for x = 0 to 1.

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see Figure 5.

Example

0.3534968007014220554658363702066982450902568008087739938078079246078001845970...

Mathematica

RealDigits[ NIntegrate[x^(1/x), {x, 0, 1}, WorkingPrecision -> 128], 10, 111][[1]] (* Robert G. Wilson v, Mar 10 2013 *)

Prog

(PARI) intnum(x=exp(-lambertw(default(realbitprecision)*log(2)+2)), 1, x^x^-1) \\ Charles R Greathouse IV, Feb 23 2022
(PARI) intnum(x=1e-9, 1, x^x^-1) \\ good for up to 29 billion digits; Charles R Greathouse IV, Feb 23 2022

Crossrefs

Cf. A073229 (decimal expansion of e^(1/e)).

Sequence in context: A374624 A210606 A254327 * A236965 A259684 A214287

Adjacent sequences: A175996 A175997 A175998 * A176000 A176001 A176002

Keyword

cons,nonn

Author

Dylan Hamilton, Nov 05 2010

Status

approved