*Fibonacci Quarterly*article by Greg Back and Mihai Caragiu ("The Greatest Prime Factor and Recurrent Sequences" - Fibonacci Quarterly 48 (2010), no. 4, 358–362) - abstract

**here**.

**In the main result on GPF-Fibonacci sequences (Theorem 3)**we prove that

*all GPF-Fibonacci sequences (that is, prime sequences in which each subsequent term is the greatest prime factor of sum of the previous two terms) that are non-constant eventually enter the same 4-cycle*

**7,3,5,2**.