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A072364 Decimal expansion of (1/e)^(1/e). 10
6, 9, 2, 2, 0, 0, 6, 2, 7, 5, 5, 5, 3, 4, 6, 3, 5, 3, 8, 6, 5, 4, 2, 1, 9, 9, 7, 1, 8, 2, 7, 8, 9, 7, 6, 1, 4, 9, 0, 6, 7, 8, 0, 2, 9, 2, 9, 7, 5, 4, 4, 7, 3, 5, 9, 3, 8, 9, 1, 4, 8, 9, 9, 9, 6, 5, 1, 7, 1, 5, 5, 9, 0, 2, 9, 0, 8, 5, 3, 6, 2, 1, 2, 3, 0, 1, 2, 3, 8, 7, 6, 4, 9, 3, 5, 3, 0, 9, 8, 3, 4, 7, 6, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Minimum value of x^x for real x>0.

Also minimum value of 1/x^(1/x) for real x>0 (occurs at e). Equals exp(Pi)/exp(1/exp(1)) * exp(-Pi). - Gerald McGarvey, Sep 21 2004

If (1/e)^(1/e) < y < 1, then x^x = y has two solutions x = a and x = b with 0 < a < 1/e < b < 1. For example, (1/e)^(1/e) < 1/sqrt(2) < 1 and (1/4)^(1/4) = (1/2)^(1/2) = 1/sqrt(2) with 1/4 < 1/e < 1/2. - Jonathan Sondow, Sep 02 2011

LINKS

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

Plouffe's Inverter entry for .69220062755

J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 3 in the link.

EXAMPLE

0.69220062755534635386...

MATHEMATICA

RealDigits[E^(-1/E), 10, 111][[1]]

PROG

(PARI) (1/exp(1))^(1/exp(1))

(PARI) exp(-1/exp(1)) \\ Charles R Greathouse IV, Sep 01 2011

CROSSREFS

Cf. A068985 (1/e), A001113 (e), A072365 ((1/3)^(1/3)), A073229 (e^(1/e)), A073230 ((1/e)^e).

Sequence in context: A195403 A021595 A197696 * A087016 A161480 A198676

Adjacent sequences:  A072361 A072362 A072363 * A072365 A072366 A072367

KEYWORD

cons,nonn

AUTHOR

Rick L. Shepherd, Jul 18 2002

STATUS

approved

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Last modified April 20 23:07 EDT 2014. Contains 240824 sequences.