User blog comment:Simply Beautiful Art/A finite variant to the Madore's OCF./@comment-5529393-20171215040530/@comment-5529393-20171216044718

If we take a number n between 0 and 2^27 - 1 and write it in binary, the 1's in the binary representation will show you which powers of 2 to take to sum to n. So n could be something like 2^19 + 2^15 + 2^13 + 2^12 + 2^10 + 2^8 + 2^3 + 2^0, and we could take the numbers 2^19, 2^15, 2^13, 2^12, and 2^10, and the remainder 2^8 + 2^3 + 2^0 is less than 1024 so we know that we can pick two numbers from C'(3) that sum to it. So we can pick seven numbers from C'(3) that sum to n; at worst, we have to pick every power of 2 from 2^10 to 2^26, so we might need to pick 19 numbers at the most.