Did you know that a TV series followed this movie? It's not a sequel, it's set in its own continuity, but it uses the same costumes and Domed City as the film, as well as reusing some of the film's footage of Carousel, but primarily follows a story almost completely disconnected from the plot of the film.
The two protagonists escape from the totalitarian city in the very first episode, and begin the formula of running into and helping out the inhabitants of the post-apocalyptic Earth, accompanied by one of this future world's non-human characters, and pursued by the city's authorities (with one enforcer given particular attention). It actually felt a whole lot like the Planet of the Apes TV series, and that description I provided was meant to apply equally to both shows. Also in common, they're set in separate timelines from their respective films, but reuse the costumes and visual design. They were also both cancelled after one 14-episode season, unfortunately, as they're both pretty good (Planet of the Apes especially). They're kind of like twins.

A very solid sci-fi flick and a pretty great movie in itself, but original books just better...

THIS IS IMPORTANT HENCE ALL CAPS:

Where can I buy that red crystal from #Logan's Run?
You know, the one that starts blinking when you are turning 30 years old?
And then "they" send you in a carrousel where you get executed and die ?!

That would be the perfect birthday present for my sister, don't you think? :P