I need to generate a controlled sequence of pseudo-random numbers, given an initial parameter. For that I\'m using the standard python random generator, seeded by this param
No, it doesn't. There's no such promise in the random module's documentation.
What the docs do contain is this remark:
Changed in version 2.3: MersenneTwister replaced Wichmann-Hill as the default generator
So a different RNG was used prior to Python 2.3.
So far, I've been using numpy.random.RandomState for reproducible pseudo-randomness, though it too does not make the formal promise you're after.
If you want full reproducibility, you might want to include a copy of random's source in your program, or hack together a "P²RNG" (pseudo-pseudo-RNG) from hashlib.