Armin Rigo added the comment:

I won't try to influence the outcome of this discussion, but I'd like to 
correct myself: in the measures I posted, "true randomness" is not needed at 
all.  The exact criterion might be hard to pin down, but as a first 
approximation, we get the same answers as long as most keys have different 
hashes, as all the bits of the hash are used by the dict lookup in only a few 
iterations.  No two small ints have the same hash, by construction.  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".


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