The density of primes dividing a particular non-linear recurrence sequence

Alexi Block Gorman, Tyler Genao, Heesu Hwang +3

Define the sequence $\{b_n\}$ by $b_0=1,b_1=1,b_2=2,b_3=1$, and $$b_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\not\equiv 0\pmod 3, \frac{b_{n-1}b_{n-3…