The Luhman 16 system is 3.52 light years from Proxima Centauri (presently). Mostly the other side of it from us. But we can image it and that's what's just been done.
So far we can see two brown dwarves orbiting a common focus. Let's call them Big Bear (33J+) and Little Bear (28J+). Proportionately, they're more evened out even than Pluto / Charon; these don't get stable L4 or L5. We have "precovery" images going from 1978's sky-survey, so we're pretty sure on their period: 27.54 years. Mutual semimajor is about 3.56 AU, with 0.343 eccentricity which is a lot: periapsis 2.34 AU. That's from the barycenter, 62J well above Big Bear's core. I want to say these planets are 4.82 AU apart when at semimajor, so Big Bear orbits over 1.26 AU away.
At 18.36 years we might see a Hilda between these two, orbiting Big Bear. A search for Neptunelikes or other perturbations hasn't come up with anything but, we haven't had that many ursine years to check; they just rule out such a monster in two-year orbits, around either. Beyond, say, 10 AU I do expect a shell of comets.
I'd be interested if either bruin has a Jovian-like system of dwarf planets. As bruins neither has any way toward an Earthlike. But Iolikes and Europalikes seem possible if such is bracketed by ice dwarfs further out in resonance. They'd have to be a bit further than our Io given either bruin's mass, but should still be secured from the other bruin. Their equivalent(s) to Callisto will have an elongate orbit. As for the mass of these subplanets, up to Mars seems possible to me.
CLOSEST 1/14: It's still the game in town. Closest game in a 65 LY search anyway...
COLONY 1/14: At three lightyears away from the nearest star obviously solar energy isn't going to work here. And I'd not count on radioactives nor on any other metals. I'd look at the bruins' magnetic fields, at the planets' geothermic, and at hydrogen fusion. But here's one fine idea: creating, feeding, and pulling energy from a black hole.
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