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%I #6 Mar 30 2012 19:00:09
%S 6,9,7,3,8,7,9,4,5,7,6,2,1,4,3,0,7,0,4,0,7,5,3,2,3,6,7,3,5,4,9,0,4,2,
%T 3,4,5,7,7,0,3,5,5,1,8,6,1,0,5,0,2,9,8,3,6,3,7,6,2,5,3,0,4,8,2,0,4,8,
%U 5,2,0,3,2,2,4,6,9,5,4,9,3,4,3,8,1,9,0,3,5,5,5,6,1,8,7,0,5,7,2,5
%N Decimal expansion of (4/9)^(4/9) = (8/27)^(8/27).
%C (4/9)^(4/9) = (8/27)^(8/27) corresponds to (9/4)^(27/8) = (27/8)^(9/4) (see A194556) under the equivalence x^x = y^y <==> (1/x)^(1/y) = (1/y)^(1/x).
%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. 8 in the link.
%e 0.6973879457621430704075323673549042345770355186105029836376253048204852032246954...
%t RealDigits[(4/9)^(4/9), 10, 100] // First
%Y Cf. A194556.
%K nonn,cons
%O 0,1
%A _Jonathan Sondow_, Sep 02 2011
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