

A277069


Decimal expansion of the real part of the root of the function x^y = y.


1



9, 9, 1, 1, 2, 0, 1, 4, 7, 9, 9, 1, 8, 7, 7, 4, 0, 4, 6, 9, 5, 2, 5, 2, 3, 9, 8, 9, 0, 4, 7, 7, 4, 4, 1, 8, 7, 2, 5, 9, 9, 7, 7, 6, 4, 1, 9, 5, 1, 3, 1, 5, 7, 5, 6, 7, 2, 3, 7, 3, 1, 2, 9, 2, 5, 9, 5, 2, 5, 4, 7, 5, 9, 9, 9, 8, 2, 5, 0, 9, 0, 9, 0, 5, 3, 1, 6, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

This value is negative.
It is not known if this number has a closed form.
This root occurs on the real component of the function x^y = y for x values which are all real.


LINKS

Table of n, a(n) for n=2..89.


FORMULA

Original fixed point function is of the form: x^y = y. When solved for y: y = ProductLog(log(x))/log(x).


EXAMPLE

99.1120147991877404695252398904774418725997764195131575672373129...


MATHEMATICA

FindRoot[Re[ProductLog[Log[x]]/Log[x]], {x, 100, 99}, WorkingPrecision > 261]


CROSSREFS

Cf. A277067.
Sequence in context: A229758 A076115 A014726 * A197503 A197401 A197350
Adjacent sequences: A277066 A277067 A277068 * A277070 A277071 A277072


KEYWORD

nonn,cons


AUTHOR

David D. Acker, Sep 27 2016


STATUS

approved



