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 A072364 Decimal expansion of (1/e)^(1/e). 11

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of (1/e)^(1/e).

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

%C 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

%C 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

%D Chin, Alex, et al., "Pick a Tree-Any Tree." The American Mathematical Monthly, 122.5 (2015): 424-432.

%H Plouffe's Inverter entry for <a href="http://oldweb.cecm.sfu.ca/cgi-bin/isc/lookup?number=.69220062755&amp;lookup_type=simple">.69220062755</a>

%H J. Sondow and D. Marques, <a href="http://arxiv.org/abs/1108.6096">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 3 in the link.

%e 0.69220062755534635386...

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

%o (PARI) (1/exp(1))^(1/exp(1))

%o (PARI) exp(-1/exp(1)) \\ _Charles R Greathouse IV_, Sep 01 2011

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

%Y Cf. also A258707.

%K cons,nonn

%O 0,1

%A _Rick L. Shepherd_, Jul 18 2002

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