Problem State: Randomized number series generation in mathematical context
               and also in application context would very useful


Solution Opportunity: Input or accept a series of numbers from the end-user ??


                      choose even or odd or pair every two alternate numbers
                      ...by making a programmatic choice at code level ...

                      ...then apply the following kind of

                                lcm or gcm or gcd or mod (modulus or reminder)

                      on each of the so derived pairs ....insert the resulting

                      results of operation on each of the pairs into a array

                      or sequence 


                      ....given the scope and context ...offers a ...good means
 
                      obtaining a randomized number series.


Note: The above problem statement having been encountered in various scenarios
      and detailed in various 'Proof of concepts' as mentioned in 
      'http://uk.geocities.com/ravivenkatus/projects.pdf' ....apply appropriate
      'use-case' modeling, rationalize and arrive at a workable and feasible 
       solution both commercially and techinically viable.