An a priori determination of serial correlation in computer generated random numbers

Background. Ever since John Von Neumann introduced the method some ten years ago 11, users of pseudo-random numbers on modern digital computers have been generating their numbers as they were required in application, rather than drawing them from a table formed beforehand or obtaining them from a special-purpose device built expressly for this service. The advantages of Von Neumann's method were its speed, minimal storage requirements, and ability to be restarted from any desired point. For some years now the mid-square method has been replaced by other recursive methods which have increased further the advantages of this general technique of generation. The most popular of these has been the multiplicative method proposed by Lehmer in 1951 2. An interesting variation of this method, which we may call the method, recently has received the attention of several authors 1, 9, 10. We adopt the notation of Coveyou, one of these authors. The mixed congruential method then may be written