The Recamán's sequence generates Natural numbers.

Starting from a(0)=0, the n'th term a(n), where n>0, is the previous term minus n i.e a(n) = a(n-1) - n but only if this is both positive and has not been previousely generated.


If the conditions don't hold then a(n) = a(n-1) + n.



Task

 Generate and show here the first 15 members of the sequence.
 Find and show here, the first duplicated number in the sequence.
 Optionally: Find and show here, how many terms of the sequence are needed until all the integers 0..1000, inclusive, are generated.


References

 A005132, The On-Line Encyclopedia of Integer Sequences.
 The Slightly Spooky Recamán Sequence, Numberphile video.
 Recamán's sequence, on Wikipedia.


recaman :: Int -> [Int]
recaman n = fst <$> reverse (go n)
  where
    go 0 = []
    go 1 = [(0, 1)]
    go x =
        let xs@((r, i):_) = go (pred x)
            back = r - i
        in ( if 0 < back && not (any ((back ==) . fst) xs)
               then back
               else r + i
           , succ i) :
           xs
 
main :: IO ()
main = print $ recaman 15