A073230 - OEIS

%I #29 Sep 08 2022 08:45:06

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

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

%U 6,3,3,0,0,3,0,7,5,6,3,0,8,1,0,4,0,8,8,2,4,2,4,5,3,3,7,1,4,6,7,7,4,5,6,7

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

%C (1/e)^e = e^(-e) = 1/(e^e) (reciprocal of A073226).

%C The power tower function f(x)=x^(x^(x^...)) is defined on the closed interval [e^(-e),e^(1/e)]. - _Lekraj Beedassy_, Mar 17 2005

%D Paul Halmos, "Problems for Mathematicians, Young and Old", Dolciani Mathematical Expositions, 1991, Solution to problem 8A (Power Tower) p. 240.

%H G. C. Greubel, <a href="/A073230/b073230.txt">Table of n, a(n) for n = 0..10000</a>

%H J. Sondow and D. Marques, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164; see the Appendix.

%e 0.06598803584531253707679018759...

%t a=IntegerDigits[IntegerPart[(1/E)^E*10^99]];PrependTo[a,0] (* _Vladimir Joseph Stephan Orlovsky_, Jul 17 2008 *)

%t RealDigits[(1/E)^E, 10, 100][[1]] (* _Alonso del Arte_, Aug 26 2011 *)

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

%o (Magma) Exp(-1)^Exp(1); // _G. C. Greubel_, May 29 2018

%Y Cf. A001113 (e), A068985 (1/e), A073229 (e^(1/e)), A072364 ((1/e)^(1/e)), A073226 (e^e).

%K cons,nonn

%O 0,2

%A _Rick L. Shepherd_, Jul 22 2002