Sometimes when I am at the gym I wonder if there could be a better set of weight denominations.
I feel like 1,3,9,27,81 could be an optimal set; but I am not sure how to prove it.
I feel like 1,3,9,27,81 could be an optimal set; but I am not sure how to prove it.
What This Country Needs is an 18¢ Piece (2002) [pdf] - https://news.ycombinator.com/item?id=38665334 - Dec 2023 (272 comments)
What This Country Needs Is an 18¢ Piece [pdf] - https://news.ycombinator.com/item?id=14579635 - June 2017 (45 comments)
So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 25, 35, 55, 75, 11*5, etc. for 5, 10, 15, 25, 35, 55, etc.
Fixed the formatting for you. You need to put a \ before * symbols to have them reliably render in HN
Alternatively, write two sequential *, like so: **
If you want to get within x% using at most k weights the some kind of logarithmic distribution is also a good bet.
Both you and OP could benefit from being a bit clearer about what you find optimal.