A valuable memory

This paper by the legendary N. J. A. Sloane mentioning the result on prime sequences (particularly GPF-Fibonacci sequences and a conjecture on GPF-Tribonacci) that I got in collaboration with my student Greg Back meant a lot to me. It is, for me, a most valuable "Math memory".

 

New paper

AN ELEMENTARY NOTE ON THE GREATEST PRIME FACTORS OF LINEARLY RELATED INTEGERS 

JP Journal of Algebra, Number Theory and Applications 

Volume 52, Issue 1, Pages 95 - 100 (October 2021) 

http://dx.doi.org/10.17654/NT052010095

New paper. GPF-Tribonacci sequences

Starting with 5, 13, 7, each subsequent term is the greatest prime factor of the sum of the previous three terms. More about this type of sequences - in a new 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.