I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 <http://oeis.org/A016037>, A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4 -- g