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 A194556 Decimal expansion of (9/4)^(27/8) = (27/8)^(9/4). 9
 1, 5, 4, 3, 8, 8, 8, 7, 3, 5, 8, 5, 5, 2, 5, 8, 3, 1, 8, 3, 6, 0, 4, 4, 6, 0, 0, 1, 3, 0, 7, 4, 9, 0, 9, 7, 1, 8, 8, 7, 1, 4, 9, 4, 2, 7, 9, 6, 8, 0, 2, 7, 2, 4, 1, 2, 8, 5, 4, 3, 3, 0, 4, 5, 3, 2, 9, 4, 4, 1, 8, 3, 6, 3, 0, 2, 2, 0, 7, 2, 0, 7, 9, 6, 9, 2, 3, 7, 0, 7, 3, 2, 6, 2, 5, 7, 6, 1, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Positive real numbers x < y with x^y = y^x are parameterized by (x,y) = ((1 + 1/t)^t,(1 + 1/t)^(t+1)) for t > 0. For example, t = 2 gives (x,y) = (9/4,27/8). See Sondow and Marques 2010, pp. 155-157. (9/4)^(27/8) = (27/8)^(9/4) corresponds to (4/9)^(4/9) = (8/27)^(8/27) (see A194789) under the equivalence x^y = y^x <==> (1/x)^(1/x) = (1/y)^(1/y). LINKS J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae, 37 (2010), 151-164. FORMULA -((9*ProductLog(-1, -(4/9)*log(9/4)))/(4*log(9/4))), where ProductLog is the Lambert W function, simplifies to 27/8. - Jean-François Alcover, Jun 01 2015 EXAMPLE 15.438887358552583183604460013074909718871494279680272412854330453294418363... MATHEMATICA RealDigits[ (9/4)^(27/8), 10, 100] // First CROSSREFS Cf. A073226 (e^e), A194557 (sqrt(3)^sqrt(27) = sqrt(27)^sqrt(3)), A194789 ((4/9)^(4/9) = (8/27)^(8/27)). Sequence in context: A092156 A086409 A202412 * A154198 A086793 A070515 Adjacent sequences:  A194553 A194554 A194555 * A194557 A194558 A194559 KEYWORD nonn,cons AUTHOR Jonathan Sondow, Aug 30 2011 STATUS approved

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