Ulam numbers

With the following initial conditions:

      u₁ = 1 
      u₂ = 2

we define the n-th Ulam number u_n as the number such that is greater than u_n-1 and uniquely written as a sum of two different Ulam numbers u_{i (<n)} and u_{j (<n)}.

Task

Write a function to generate the n-th Ulam number.

References

OEIS Ulam numbers

Haskell

Lazy List

<lang haskell> ulam

 :: Integral i =>
    Int -> i

ulam 1 = 1 ulam 2 = 2 ulam n

 | n > 2 = ulams !! (n-1)

ulams

 :: Integral n =>
    [n]

ulams = 1:2:(nexts [2,1]) nexts us = u: (nexts (u:us))

 where
   n = length us
   [u] = head . filter isSingleton . group . sort  $ 
           [v | i <- [0 .. n-2], j <- [i+1 .. n-1] 
              , let s = us !! i
              , let t = us !! j
              , let v = s+t
              , v > head us
              ]

isSingleton :: [a] -> Bool isSingleton as

 | length as == 1 = True
 | otherwise      = False