A -number is a Real Number such that
See also Collatz Problem
References
Flatto, L. ``-Numbers and -Transformations.'' Symbolic Dynamics and its Applications, Contemporary
Math. 135, 181-201, 1992.
Guy, R. K. ``Mahler's -Numbers.'' §E18 in Unsolved Problems in Number Theory, 2nd ed.
New York: Springer-Verlag, p. 220, 1994.
Lagarias, J. C. ``The Problem and its Generalizations.'' Amer. Math. Monthly 92, 3-23, 1985.
http://www.cecm.sfu.ca/organics/papers/lagarias/.
Mahler, K. ``An Unsolved Problem on the Powers of 3/2.'' Austral. Math. Soc. 8, 313-321, 1968.
Tijdman, R. ``Note on Mahler's
-Problem.'' Kongel. Norske Vidensk Selsk. Skr. 16, 1-4,
1972.