login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072364 Decimal expansion of (1/e)^(1/e). 10

%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://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).

%K cons,nonn

%O 0,1

%A _Rick L. Shepherd_, Jul 18 2002

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 07:52 EST 2014. Contains 250285 sequences.