29 lines
912 B
Haskell
29 lines
912 B
Haskell
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-- What is most surprising is that the important mathematical constant,
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-- e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...].
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--
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-- The first ten terms in the sequence of convergents for e are:
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-- 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ...
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--
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-- The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17.
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--
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-- Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.
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s = 2:rest 1
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where rest k = 1:2*k:1:rest (k+1)
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calc (x:[]) = (x,1)
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calc (x:xs) = let
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precalc = calc xs
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num = fst precalc
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den = snd precalc
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in
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(x * num + den, num)
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sumText :: Integer -> Integer
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sumText bignum = sum $ map (\x -> read (x:[]) :: Integer) $ show bignum
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main = do
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-- print $ sumText $ fst $ calc $ take 10 s
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print $ sumText $ fst $ calc $ take 100 s
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