Generating sorted list of all possible coprimes

Question

I need to generate infinite sorted list of all coprimes. The first element in each pair must be less than the second. The sorting must be done in ascending order -- by the sum o

Answer 1

While probably not the most optimal way it should works if you first generate all possible pairs and then filter them.

So using your criteria:

pairs :: [(Integer,Integer)]
pairs = [ (i,l-i) | l <- [1..], i <- [1..l-1] ]

coprimes :: [(Integer,Integer)]
coprimes = [ (i,j) | (i,j) <- pairs, 1 < i, i < j,gcd i j == 1]

produces

λ> take 10 coprimes
[(2,3),(2,5),(3,4),(3,5),(2,7),(4,5),(3,7),(2,9),(3,8),(4,7)]

now of course you can put some of the stuff 1 < i and i < j comes to mind into the pairs definition or even join them but I think here it's more obvious what's going on