57 lines
1.4 KiB
Haskell
57 lines
1.4 KiB
Haskell
import Data.Numbers.Primes (isPrime)
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----------------------- PELL SERIES ----------------------
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pell :: Integer -> Integer -> [Integer]
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pell a b = a : b : zipWith (+) (pell a b) ((2 *) <$> tail (pell a b))
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a000129, a002203, a001333, a086383, a096650, a002315 :: [Integer]
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a000129 = pell 0 1
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a002203 = pell 2 2
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a001333 = (`div` 2) <$> a002203
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a086383 = filter isPrime a000129
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a096650 = zip [0 ..] a000129 >>= (\(i, n) -> [i | isPrime n])
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a002315 = 1 : 7 : zipWith (-) ((6 *) <$> tail a002315) a002315
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------------------- PYTHAGOREAN TRIPLES ------------------
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pythagoreanTriples :: [(Integer, Integer, Integer)]
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pythagoreanTriples =
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(tail . concat) $ zipWith3 go [0 ..] a000129 (scanl (+) 0 a000129)
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where
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go i p m
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| odd i = [(m, succ m, p)]
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| otherwise = []
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-------------------------- TESTS -------------------------
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main :: IO ()
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main = do
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mapM_
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(\(k, xs) -> putStrLn ('\n' : k) >> print (take 10 xs))
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[ ("a000129", a000129)
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, ("a002203", a002203)
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, ("a001333", a001333)
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-- Waste of electrical power ?
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-- ("a086383", a086383)
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-- ("a096650", a096650
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, ("a002315", a002315)
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]
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putStrLn "\nRational approximations to sqrt 2:"
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mapM_ putStrLn $
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(take 10 . tail) $
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zipWith
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(\n d ->
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show n <>
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('/' : show d) <> " -> " <> show (fromIntegral n / fromIntegral d))
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a001333
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a000129
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putStrLn "\nPythagorean triples:"
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mapM_ print $ take 10 pythagoreanTriples
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