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

You can try enumerating all pairs of integers. This code is based in the enumeration described at University of California Berkeley (doesn't include 0)

data Pair=Pair Int Int deriving Show

instance Enum Pair where
    toEnum n=let l k=truncate (1/2 + sqrt(2.0*fromIntegral k-1))
                 m k=k-(l k-1)*(l k) `div` 2
             in 
               Pair (m n) (1+(l n)-(m n))
    fromEnum (Pair x y)=x+((x+y-1)*(x+y-2)) `div` 2

But you can use another enumeration.

Then you can do:

[2*n+3*m+1|Pair n m<-map toEnum [1..]]