OFFSET
1,2
COMMENTS
It is unknown if this root is rational, algebraic irrational, or transcendental.
LINKS
J. Marshall Ash and Yiren Tan, A rational number of the form a^a with a irrational, Mathematical Gazette 96, March 2012, pp. 106-109.
Wikipedia, Tetration, Open questions
EXAMPLE
1.4466014324298641745973339875976614806873210422822800263639...
MATHEMATICA
RealDigits[FindRoot[x^x^x^x == 2, {x, 1}, WorkingPrecision -> 110][[1, 2]], 10, 105][[1]]
PROG
(PARI) solve(x=1, 2, x^x^x^x-2) \\ Charles R Greathouse IV, Apr 15 2014
CROSSREFS
KEYWORD
AUTHOR
Vladimir Reshetnikov, Apr 29 2013
STATUS
approved