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A277053 Decimal expansion of real zero x between 78 and 79 of the derivative of the function plotting the invariant points for the exponential function of the form x^y = y. 0
7, 8, 5, 1, 7, 6, 6, 8, 8, 7, 3, 3, 8, 0, 6, 8, 5, 1, 9, 2, 8, 2, 9, 7, 5, 9, 9, 9, 0, 3, 9, 1, 9, 9, 3, 7, 6, 0, 0, 4, 9, 5, 9, 5, 1, 3, 1, 9, 5, 8, 9, 3, 6, 7, 1, 5, 5, 8, 0, 1, 1, 0, 8, 4, 7, 3, 5, 2, 7, 1, 7, 3, 1, 2, 6, 0, 6, 7, 6, 3, 0, 0, 6, 4, 2, 6, 8, 9, 0, 6, 0, 7, 5, 1, 8, 8, 1, 6, 1, 7, 7, 8, 2, 3, 9, 7, 2, 2, 3, 9, 1, 7, 7, 4, 3, 0, 2, 7, 7, 7, 7, 5, 8, 2, 4, 0, 4, 0, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

It has not yet been determined if this number has a closed form.

LINKS

Table of n, a(n) for n=2..131.

FORMULA

The derivative x^y = y, or y = -ProductLog(-Log(x))/Log(x) when solved for y, is the function in which this value is a root. The derivative is (ProductLog(-Log(x))^2)/((x*Log(x)^2)*(1+ProductLog(-Log(x))).

EXAMPLE

78.5176688733806851928297599903919937600495951319589367155801108473527173126...

MATHEMATICA

FindRoot[Re[ProductLog[-Log[x]]^2/(x Log[x]^2 (1 + ProductLog[-Log[x]]))], {x, 78, 79},

WorkingPrecision -> 261]

CROSSREFS

Cf. A042972, A073229.

Sequence in context: A019794 A020829 A109916 * A076415 A190573 A216542

Adjacent sequences:  A277050 A277051 A277052 * A277054 A277055 A277056

KEYWORD

nonn,cons

AUTHOR

David D. Acker, Sep 26 2016

STATUS

approved

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Last modified September 20 21:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)