[Armin]
> You can build a sequence of (long) integers that have all exactly the
> same hash, but doing that is not as easy as "2**k".

Sure it is.  The hash for integers is (by design) repeated modulo a number of the form 2**n - 1:  we use 2**61 - 1 on 64-bit systems and 2**31 - 1 on 32-bit.  So in {2**k for k in range(n)} you get at most 61 distinct hash values.