OFFSET
1,1
COMMENTS
The larger solution is of course 3.
Also, the limit of infinite tetration a^a^...^a of a=3^(1/3) (=A002581), i.e., lim_{n->oo} x(n) where x(n+1)=a^x(n), x(1)=a. - M. F. Hasler, Nov 03 2013
The constant is transcendental (Vassilev-Missana, p. 23). - Peter Bala, Jan 01 2014
LINKS
M. Vassilev-Missana, Some results on infinite power towers, Notes on Number Theory and Discrete Mathematics, Vol. 16 (2010) No. 3, 18-24.
EXAMPLE
2.47805268028830241189373651689...
MATHEMATICA
RealDigits[ -3*ProductLog[ -Log[3]/3 ] / Log[3], 10, 105] // First (* Jean-François Alcover, Mar 05 2013 *)
PROG
(PARI) solve(x=2, exp(1), 3^x-x^3)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Franklin T. Adams-Watters, Oct 23 2009
STATUS
approved