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 $n>16$.
List of the minimal addition chains
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sequences-and-series
combinatorics
reference-request
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0@Srivatsan Agreed and updated, didn't even know about those tags! – 2012-04-03
2 Answers
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See https://oeis.org/A003313 and references there, in particular the table up to n=10001.
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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.
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1Thanks @DaveBall. Note that the reference is also in the OEIS link provided by RobertIsrael. – 2012-04-12