  The aim of this paper is to show a peculiar behavior of a (hypothetical)
Collatz sequence going to infinity. We study the associated Syracusa sequence
(the odd elements of the former) and show that the limit set of a conveniently
normalized sequence is the whole unit interval. In particular, for any positive
integer there is a subsequence whose elements' expansions in base 3 begin (from
the left) with the expansion of the given number.
