## Prime Generating Sequences

A couple of months ago (really, a long, long time ago) I found an interesting question on Mathematics Stack Exchange (another site to effectively waste away hours of your life). It reminded me of my Bachelor’s thesis (which I wrote a really, really long time ago) about the sequence $g_n=\mathrm{gcd}(n,a_{n-1})=(n,a_{n-1}) \quad\text{for}\quad n>1,$ where $$a_1=7$$ and $a_n=a_{n-1}+g_n.$ Here, $$\mathrm{gcd}(a,b)=(a,b)$$ stands for the greatest common divisor,1 i.e., the largest integer $$d$$ that divides both $$a$$ and $$b$$. [Read More]