

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
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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



