The density of primes dividing a term in the Somos-5 sequence

Bryant Davis, Rebecca Kotsonis, Jeremy Rouse

The Somos-5 sequence is defined by $a_0=a_1=a_2=a_3=a_4=1$ and $a_m=\frac{a_{m-1}{a}_{m-4}+a_{m-2}{a}_{m-3}}{a_{m-5}}$ for $m\ge 5$. We relate the arithme…