According to this Time article [1], people who sleep between 6.5 and 7.5 hours a night live the longest. The following program computes optimal amounts of time to sleep for both naps and nighttime. The variable circadian was chosen to be 21.83 because for n = 8 it gives almost exactly 24 hours and for n = 6 it gives 7 hours and 14 minutes. This …

nap.hs

{-
 - Usage: ./nap [INT]
 - [INT] is some positive integer (eg 1, 2, etc)
 -}

import System.Environment (getArgs)
import Control.Applicative ((<$>), (<*>), pure)

circadian = 21.83

naptime :: Double -> Double
naptime x = (circadian ** x) * (12 ** (1-x))

main :: IO ()
main = argv 0 >>= putStrLn . fmttime . naptime . read
    where argv :: Int -> IO String
          argv n = (!!) <$> getArgs <*> pure n

fmttime :: Double -> String
fmttime t = pr ++ (show ms) ++ " minutes"
    where t' = fromIntegral . floor $ t
          hs = t' `div` 60
          ms = t' - (hs * 60)
          pr = case hs of
                 0 -> ""
                 1 -> show hs ++ " hour and "
                 _ -> show hs ++ " hours and "