Wikipedia says:
LHS 1140 is a red dwarf in the constellation of Cetus…The star is over 5 billion years old and has 15% of the mass of the Sun. LHS 1140’s rotational period is 130 days…LHS 1140 is known to have two confirmed rocky planets orbiting it, and a third candidate planet not yet confirmed.
Planet b was in the media spotlight in 2017:
LHS 1140b: Potentially Habitable Super-Earth Found Orbiting Nearby Red Dwarf – Sci-News.
“This is the most exciting exoplanet I’ve seen in the past decade,” said Dr. Jason Dittmann, an astronomer at the Harvard-Smithsonian Center for Astrophysics and lead author of the Nature paper.
. . .
“The LHS 1140 system might prove to be an even more important target for the future characterization of planets in the habitable zone than Proxima b or TRAPPIST-1,” concluded co-authors Dr. Xavier Delfosse and Dr. Xavier Bonfils, both at the CNRS and IPAG in Grenoble, France.
Let’s take a look at the orbital data after the latest update last week (source: exoplanet.eu):
1140 c orbits in 3.777931 days
1140 b orbits in 24.736 days
275 c = 1038.931 d
42 b = 1038.912 d
Conjunctions per period = 275 – 42 = 233
275 = 55*5
42 = 21*2
2,5,21,55 and 233 are all Fibonacci numbers.
The ratio of one c-b conjunction to 5 c orbits is 1:Phi³(or 233/55).
A final point of interest:
8 rotations of star LHS 1140 = 8*130 = 1040 days, only a day more than the selected orbital period. 8 is also a Fibonacci number.
That raises the question of whether the planetary conjunctions are synchronized with the solar rotation period in this system.
Tallbloke's Talkshop 
Wowser. Great work OB.
OB, I put forth a rather discrete challenge: See if you can generalize your approach to simply take as inputs planetary periods and spit out standard formula coefficients. I know from work I’ve done that this is possible. There’s little chance I’ll finish the work. As soon as I’m sure of the existence of an aggregate proof I’m satisfied and looking around for new avenues to explore. I’ll still post a few more 5256 gems because they were the keys I found far from the “light” of the conventional lamp post.
With exoplanets the data is not always reliable. This pair were found in 2017 and there was an update last week, but what was updated isn’t stated. A third planet is unconfirmed.
The Dance Of Jupiter’s Moons
May 18, 2020 Caltech
One open question still puzzles planetary scientists: How did the Jovian satellites form?
‘Now, Caltech professor of planetary science Konstantin Batygin (MS ’10, PhD ’12) and his collaborator Alessandro Morbidelli of Observatoire de la Côte d’Azur in France have proposed an answer to this longstanding question. Using analytical calculations and large-scale computer simulations, they propose a new theory of the Jovian satellites’ origins. The research is described in a paper appearing in the May 18 issue of The Astrophysical Journal.’
https://scienceblog.com/516433/the-dance-of-jupiters-moons/
Another one in our own system: Thule (126 km. wide).
Thule was the first discovered member of the Thule dynamical group, which as of 2008 is known to consist of three objects: 279 Thule, (186024) 2001 QG207, and (185290) 2006 UB219.[4] The orbits of these bodies are unusual. They orbit in the outermost edge of the asteroid belt in a 4:3 orbital resonance with Jupiter, the result of the periodic force Jupiter exerts on a body with Thule’s orbital period, in the same way (though with the reverse effect) as the Kirkwood gaps in the more inner parts of the asteroid belt.
https://en.wikipedia.org/wiki/279_Thule
It’s more like 17:13 than 4:3, and rotates at almost the same rate (0.9957 d) as Earth.