A258504 - OEIS

%I #5 Jun 01 2015 14:45:21

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

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

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

%N Decimal expansion of (27/64)^(27/64) = (81/256)^(81/256).

%H Jonathan Sondow, Diego 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

%F x^x = y^y <==> (1/x)^(1/y) = (1/y)^(1/x), hence, from A258503:

%F (64/27)^(256/81) = (256/81)^(64/27) <==> (27/64)^(27/64) = (81/256)^(81/256).

%e 0.6948233607279167955009391708983145471565914206815539940260405544...

%t RealDigits[(27/64)^(27/64), 10, 105] // First

%Y Cf. A194556, A194789, A258503.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jun 01 2015