Common defects in initialization of pseudorandom number generators

We demonstrate that a majority of modern random number generators, such as the newest version of rand.c, ranlux, and combined multiple recursive generators, have some manifest correlations in their outputs if the initial state is filled up using another linear recurrence with similar modulus. Among 58 available generators in the GNU scientific library, 40 show such defects. This is not because of the recursion, but because of carelessly chosen initialization schemes in the implementations. A good initialization scheme eliminates this phenomenon.