Prime-generating recurrence

This Demonstration explores solutions of the recurrence a(n)=a(n-1)+gdc(n,a(n-1)) through the difference sequence a(n)-a(n-1), which exhibits complex behavior. For the initial condition a(1)=7, the sequence a(n)-a(n-1) consists entirely of 1s and primes, making this recurrence a rare "naturally occurring" generator of primes. This result is not true in general: for example, letting a(1)=800 produces a(21)-a(20)=21, and letting produces . However, for these initial conditions, the difference sequence eventually consists entirely of 1s and primes. It is an unsolved problem to determine whether all initial conditions eventually produce only 1s and primes. You can choose to view all terms of the difference sequence or only the terms which are not 1Prime NumbersComponente Curricular::Ensino Fundamental::Séries Finais::Matemátic