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A194557
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Decimal expansion of sqrt(3)^sqrt(27) = sqrt(27)^sqrt(3).
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7
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1, 7, 3, 6, 1, 9, 0, 5, 2, 5, 0, 9, 5, 3, 1, 3, 5, 2, 1, 5, 4, 1, 5, 7, 1, 4, 8, 2, 6, 8, 3, 3, 2, 6, 7, 5, 8, 2, 2, 9, 5, 5, 3, 2, 1, 8, 4, 8, 9, 0, 8, 6, 4, 0, 7, 8, 4, 5, 4, 6, 9, 6, 0, 5, 7, 4, 4, 6, 7, 6, 3, 7, 4, 5, 8, 4, 3, 3, 5, 6, 3, 1, 2, 3, 2, 3, 4, 2, 1, 7, 1, 0, 0, 6, 1, 8, 3, 5, 2, 5
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OFFSET
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2,2
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COMMENTS
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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 = 1/2 gives (x,y) = (sqrt(3),sqrt(27)). See Sondow and Marques 2010, pp. 155-157.
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LINKS
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FORMULA
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-((2*sqrt(3)*ProductLog(-1, -(log(3)/(2*sqrt(3)))])/log(3)), where ProductLog is the Lambert W function, simplifies to sqrt(27). - Jean-François Alcover, Jun 01 2015
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EXAMPLE
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17.361905250953135215415714826833267582295532184890864078454696057446763745...
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MATHEMATICA
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RealDigits[ Sqrt[3]^Sqrt[27], 10, 100] // First
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CROSSREFS
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Cf. A073226 (decimal expansion of e^e), A194556 (decimal expansion of (9/4)^(27/8) = (27/8)^(9/4)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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