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Testing for randomness

It's hard to tell what you're looking for.  There are some white noise tests
in time series, some of which, I imagine, are implemented in some of the
time series packages for R.  There are tests for quality of pseudo-random
number generators, probably the best known being Marsaglia's DIEHARD battery
of tests.  You can find them by googling.  They are not in R, though, AFAIK.

Andy