Problem 65, that was easy!

065.hs

@@ -0,0 +1,28 @@
+-- What is most surprising is that the important mathematical constant,
+-- e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...].
+-- 
+-- The first ten terms in the sequence of convergents for e are:
+-- 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ...
+-- 
+-- The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17.
+-- 
+-- Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.
+
+
+s = 2:rest 1
+    where rest k = 1:2*k:1:rest (k+1)
+
+calc (x:[]) = (x,1)
+calc (x:xs) = let 
+                precalc = calc xs
+                num = fst precalc
+                den = snd precalc
+              in
+                (x * num + den, num)
+    
+sumText :: Integer -> Integer
+sumText bignum = sum $ map (\x -> read (x:[]) :: Integer) $ show bignum
+
+main = do
+    -- print $ sumText $ fst $ calc $ take 10 s
+    print $ sumText $ fst $ calc $ take 100 s