How common or rare is the double-denarius in its earliest releases? Caracalla, Macrinus, Diadumenian, Elagabalus, Severus Alexander, Maximinus Thrax, Maximus, Pupienus, Balbinus? Did the Gordians even mint them or just the denarius.
All issues of antoniniani before Gordian III are scarce to very rare. On the flip side the denarii after Gordian III are scarce to very rare, especially in good silver.
There are some very rare denarii of Philip I, IIRC, and the denarius continued intermittently, mostly as a base metal coin and as possibly a special occasion coin, until 294. I'm not sure if Diocletian issued any special occasion denarii. I'd have to open Sear. AE Denarii of Aurelian are affordable.
There are denarii up till Gallienus, although mostly bronze. However few emperors after Gordian III minted them, Philip I being the last one with the debased silver content around 40%. Good luck finding one as they rarely come up at auction and always sell for a couple thousand.