A277067 Decimal expansion of value of x such that the solution y to the equation x^y = y has equal real and imaginary parts.

7, 5, 0, 0, 4, 5, 2, 5, 6, 4, 6, 0, 1, 5, 1, 7, 1, 1, 2, 3, 7, 8, 5, 2, 9, 9, 3, 0, 3, 6, 8, 2, 2, 4, 1, 5, 5, 2, 5, 2, 1, 0, 9, 6, 1, 0, 7, 5, 1, 4, 7, 2, 5, 0, 9, 3, 7, 2, 0, 5, 3, 1, 7, 9, 8, 2, 7, 9, 3, 7, 7, 4, 6, 5, 3, 7, 8, 1, 1, 3, 7, 8, 4, 0, 8, 2, 1, 1, 7, 4, 9, 2, 1, 1, 6, 1, 5, 9, 4, 8, 7, 8, 3

Offset

0,1

Comments

It is not known if this number has a closed form.

Links

Table of n, a(n) for n=0..102.

Formula

The solution to x^y=y is y=-ProductLog(-log(x))/log(x).

Example

-0.750045256460151711237852993036822415525210961075147250937205...

Mathematica

FindRoot[Re[-ProductLog[-Log[x]]/Log[x]] - Im[-ProductLog[-Log[x]]/Log[x]], {x, -0.76, -0.74}, WorkingPrecision -> 261]

Crossrefs

Cf. A042972, A073229, A277069.

Sequence in context: A374295 A100976 A152627 * A354823 A241902 A356023

Adjacent sequences: A277064 A277065 A277066 * A277068 A277069 A277070

Keyword

cons,nonn

Author

David D. Acker, Sep 27 2016

Status

approved