The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath Conjecture for prime numbers. We introduce a natural extension of the original triangular arrangement, obtaining a growing hexagonal covering of the plane. We focus on the sequence of Square-Primes (products of squares and primes) and derive some preliminary results on these numbers. We also prove results on their distribution and provide some conjectures. This is joint work with Alexandru Zaharescu and Cristian Cobeli.

Talk by Raghavendra Bhat.