J. Shallit (2003). "What this country needs is an 18c piece" (PDF). Mathematical Intelligencer. 25 (2): 20–23.

What readers of your comment need is two HN thread references :)

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)

Since every positive even integer is the sum of two primes (at least, within the range of weights you're likely to be lifting), maybe [5, ...the list of primes times 5]?

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.

> So if the list of primes is 2, 3, 5, 7, 11, etc, you could have weights of 5, 2*5, 3*5, 5*5, 7*5, 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

> You need to put a \ before * symbols to have them reliably render in HN

Alternatively, write two sequential *, like so: **

By the time I'm on my third set, math with multiples of 5 is hard; please don't make me use those...

Optimal in what sense? If you want to have each whole number using each number at most twice then sure.

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.

See this comment for a more in-depth explanation of what I meant by "optimal" for poker chip denominations. Hopefully that clarifies. That comment has a link to the code if it's still not clear enough.

https://news.ycombinator.com/item?id=40576198