How to express {2n+3m+1|n,m∈N} in list comprehension form? (N is the set of natural numbers including 0)

Question

How do I express {2n+3m+1|n,m∈N} in list comprehension form? N is the set of natural numbers, including 0.

Answer 1

my 0.2:

trans = concat [ f n | n <- [1..]]
 where 
  mklst x = (\(a,b) -> a++b).unzip.(take x).repeat
  f n | n `mod` 2 == 0 = r:(mklst n (u,l))
      | otherwise      = u:(mklst n (r,d))
  u = \(a,b)->(a,b+1)
  d = \(a,b)->(a,b-1)
  l = \(a,b)->(a-1,b)
  r = \(a,b)->(a+1,b)

mkpairs acc (f:fs) = acc':mkpairs acc' fs
                  where acc' = f acc
allpairs = (0,0):mkpairs (0,0) trans          
result = [2*n + 3*m + 1 | (n,m) <- allpairs]