F

Aside from focusing on F1 cars and competition, they are also similar for aesthetics (Capeta is more recent but has a vintage look). Both are underdog sports stories in which the bond between a fiery teenage boy and his father plays an important part. 

I would only recommend F if you understand spoken Japanese well as the subbed versions that I have found are trash. However, if you can understand what is being said, then F is a fantastic watch as F is another anime featuring racing that has very good character development. While Initial D features Takumi, a spacey dude who has not yet found his love of racing, F has his polar opposite Gunma, a fiery guy who is determined to be the fastest in the world. I was surprised at how much I enjoyed F, to the point where I think the reason why it doesn't have a bigger MAL community is because of MAL's two character minimum search (half-joking). If you watch Initial D for the eurobeat races though, this recommendation may not apply to you. read more 

FORMULA 1!!!! 

It is obvious that the author of F was inspired by the ANJ. Both have a cocky protagonist The main rivals are also similar