The question of finding the Minimal Addition Chain (MAC) for needed for Addition chain exponentiation seems to be NP-complete. As such, it would be nice to have a list for the small powers already computed. Wikipedia lists the MAC's for $n\le16$. I'm looking for the known MAC's for $n>16$.
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See https://oeis.org/A003313 and references there, in particular the table up to n=10001.
This site about shortest addition chains lets you generate a shortest addition chain for any number < 2^27, and lists a lot of interesting properties and references about them.