a_math_guy

I don't get the 2nd "subsequence": why not iff every subsequence converges to x? It is problem #12, p. 39 of Royden's Real Analysis 3rd ed.

I want to program an exhuastive search through the partition of an integer n with a fixed number of terms k and specific properties (e.g., run through all partitions of 100001 with 125 non-equal odd terms). I would like to know if there is an easy programming strategy.

I have got an idea about how I could do it (like chewing away at the left with borrowing---start with the list [1,3,5,...,the remainder at the end] then see where is the first position on the left where you can borrow a 2, etc.) but programming that seems a little messy so I as wondering about an easy way to do it.

Something similar to using the numbers n between 0 and 2^n-1 to get subsets (bit k of n is 0/1 means element k is out/in of subset).......

Given a Gaussian integer z and a radius R, I want to find the smallest-normed Gaussian integer L such that every Gaussian integer within radius R of z shares a common factor with L.

The simplest greedy algorithm would be to repeatedly multiply in prime factors present in a list of non-covered points within the circle that have smallest norm until you have covered all points within the circle. I was trying to refine this concept with a weighting process but couldn't clarify the concept well. I was thinking that if prime p with norm P covered one point but prime q with norm Q=P+e covered two points where e was small, then it would be better to include q than p in the product. But trying to figure out the proper formula for a weighting function made it sound like an exhuastive search through a network.

Any suggestions? My first simple guess was: value of using prime p would be P^(1/n) where n=# of uncovered points that have a factor of prime p.