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%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]
%H Plouffe's Inverter entry for <a href="http://bootes.math.uqam.ca/cgi-bin/ipcgi/lookup.pl?Submit=GO+&number=0.69220062755&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).
%K cons,nonn,changed
%O 0,1
%A _Rick L. Shepherd_, Jul 18 2002
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