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A072364
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Decimal expansion of (1/e)^(1/e).
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14
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6, 9, 2, 2, 0, 0, 6, 2, 7, 5, 5, 5, 3, 4, 6, 3, 5, 3, 8, 6, 5, 4, 2, 1, 9, 9, 7, 1, 8, 2, 7, 8, 9, 7, 6, 1, 4, 9, 0, 6, 7, 8, 0, 2, 9, 2, 9, 7, 5, 4, 4, 7, 3, 5, 9, 3, 8, 9, 1, 4, 8, 9, 9, 9, 6, 5, 1, 7, 1, 5, 5, 9, 0, 2, 9, 0, 8, 5, 3, 6, 2, 1, 2, 3, 0, 1, 2, 3, 8, 7, 6, 4, 9, 3, 5, 3, 0, 9, 8, 3, 4, 7, 6, 0, 4
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OFFSET
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0,1
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COMMENTS
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Minimum value of x^x for real x>0.
Also minimum value of 1/x^(1/x) for real x>0 (occurs at e). Equals exp(Pi)/exp(1/exp(1)) * exp(-Pi). - Gerald McGarvey, Sep 21 2004
If (1/e)^(1/e) < y < 1, then x^x = y has two solutions x = a and x = b with 0 < a < 1/e < b < 1. For example, (1/e)^(1/e) < 1/sqrt(2) < 1 and (1/4)^(1/4) = (1/2)^(1/2) = 1/sqrt(2) with 1/4 < 1/e < 1/2. - Jonathan Sondow, Sep 02 2011
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LINKS
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FORMULA
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Equals Sum_{k>=0} (-1)^k/(exp(k)*k!).
Equals Product_{k>=0} exp((-1)^(k+1)/k!). (End)
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EXAMPLE
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0.69220062755534635386...
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MAPLE
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MATHEMATICA
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RealDigits[E^(-1/E), 10, 111][[1]]
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PROG
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(PARI) (1/exp(1))^(1/exp(1))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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