Problem 64

64.hs

@@ -0,0 +1,16 @@
+next :: (Integer, Integer, Integer) -> (Integer, Integer, Integer)
+next (a, b, n) = let nextA = (n - b * b) `div` a
+                     nextB = nextA * ceiling((sqrt (fromIntegral n) + fromIntegral b) / fromIntegral nextA - 1) - b
+                 in (nextA, nextB, n)
+
+hasOddPeriod :: Integer -> Bool
+hasOddPeriod n = let sqrtn   = floor . sqrt . fromIntegral $ n
+                     initial = (1, sqrtn, n)
+                 in if sqrtn * sqrtn == n 
+                    then False
+                    else odd . (+1) . length $ takeWhile (initial /=) (tail $ iterate next initial)
+
+numOfOddPeriods :: Integer -> Int
+numOfOddPeriods n = length $ filter (== True) $ map hasOddPeriod [2..n]
+
+main = print $ numOfOddPeriods 10000