Proof isn't always possible

Pyramid schemes and the related Ponzi scheme both have much in common with the number of seeks in a binary lookup on a sorted list. To expand, we can calculate how many levels of ten member groups you could hope to describe under ideal conditions in a given population— 340,000,000 OR 8 x 10^10. To be sure, we can compare it to 12 member groups (nested) and “back up” to 5 member groups (just in case).  The label “multi lever marketing” or MLM more exactly covers this arrangement, but what ever the case, we expect that practical numbers can deter blind participation in a Ponzi scheme “bubble,” if properly disseminated.

Recursion as a principle shows up in Statistics and object oriented programming. In programming it might be memory intensive and intricate, but in the abstract, these solutions have the beauty and allure of elegance. A recursive application of modulo division is another solution in search of an application in mathematics. Fibonacci wrote a whole book about the Fibonacci series, on the slender basis of a use in censuses. So to contrive an application of recursive modulo division, we assert the smoker who collects cigarette butts. For every seven butts he collects, he can roll one supplemental cigarette. Recursion becomes useful when he smokes these, but remembers to collect these butts as well, revisiting his solution. Note: as a practical matter, we add the resulting tally of butts to the modulo remaining unused butts, for a new arithmetical exercise. Ex: At the observatory a scientist collects as many butts as there are three digit primes. He performs his experiment on these, as ...