## 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 \(b\).
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