Ha. I was wondering when someone would notice that!
It doesn't exist. Yet.
Imagine an FF with a motorcycle engine, weighs 950 with driver. 1-liter engine restricted to make 115 HP (probably about 7500 RPM). Use 13x6 wheels and a hard-compound FF tire (such as the American Racers). Does FF lap times. Compatible with FF both in corners and down the straights (i.e. can be grouped together safely).
Another way of looking at it is: an F1000 without wings, restrictor on the engine, and wheels and tires as above.
Optionally put on a sports racer body. In other words, a P2 MC car without down-force, restrictor on the engine, and wheels and tires as above.
This has been discussed many times on apexspeed over the years. See these threads:
"Formula D", "Open Wheel Miata", "Phoenix FS FS600", "The cheapest practical SR2", "Entry Level Formula Car", and "FS1000 Scalable to FB", "P3". The cars have been called "FD", "Formula Super 600", and "FS1000".
I'm interested in the version with a sports-racer body, which I'm calling "Prototipo Super Leggero", meaning super-light prototype. 'cause, you know, Italian's always cool when it comes to race cars.
I believe it's a cost-sweat-spot, and could get more people into the sport.
I'm going to build one in order to demonstrate the concept and to get the tires, springs, shocks, engine HP, and so on figured out. I think I will start with an older DSR, like a first-gen Stohr.