Solve 'Pure odd digits primes' kata

Author: borisskert

src/Codewars/G964/Pureoddprime.hs

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+module Codewars.G964.Pureoddprime (onlyOddDigPrime) where
+
+-- https://www.codewars.com/kata/55e0a2af50adf50699000126/train/haskell
+
+import Data.List (genericLength)
+
+onlyOddDigPrime :: (Integral a) => a -> [a]
+onlyOddDigPrime n = [genericLength lowerSeq, last lowerSeq, head greaterSeq]
+  where
+    greaterSeq = dropWhile (<= n) oddDigPrimeSeq
+    lowerSeq = takeWhile (<= n) oddDigPrimeSeq
+
+oddDigPrimeSeq :: (Integral a) => [a]
+oddDigPrimeSeq = filter hasOddDigits primeSeq
+
+primeSeq :: (Integral a) => [a]
+primeSeq = 2 : filter isPrime [3, 5 ..]
+
+isPrime :: (Integral a) => a -> Bool
+isPrime n
+  | n <= 1 = False
+  | n <= 3 = True
+  | even n || n `mod` 3 == 0 = False
+  | otherwise = not (any divides [5, 7 .. limit])
+  where
+    limit = sqrtInt n
+    divides i = n `mod` i == 0 || n `mod` (i + 2) == 0
+
+sqrtInt :: (Integral a) => a -> a
+sqrtInt n = round $ sqrt . fromIntegral $ n
+
+hasOddDigits :: (Integral a) => a -> Bool
+hasOddDigits = all (odd . (`mod` 2)) . digits
+
+digits :: (Integral a) => a -> [a]
+digits 0 = []
+digits n = digits (n `div` 10) ++ [n `mod` 10]

test/Codewars/G964/PureoddprimeSpec.hs

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+module Codewars.G964.PureoddprimeSpec where
+
+import Codewars.G964.Pureoddprime (onlyOddDigPrime)
+import Test.Hspec
+import Test.QuickCheck
+import Text.Printf (printf)
+
+testOPS :: Integer -> [Integer] -> Spec
+testOPS n s =
+  it (printf "should return onlyOddDigPrime for n result : %d --> %s \n" n (show s)) $
+    onlyOddDigPrime n `shouldBe` s
+
+spec :: Spec
+spec = do
+  describe "Basic tests onlyOddDigPrime" $ do
+    testOPS 20 [7, 19, 31]
+    testOPS 40 [9, 37, 53]
+    testOPS 55 [10, 53, 59]
+    testOPS 60 [11, 59, 71]
+    testOPS 100 [15, 97, 113]
+    testOPS 5333 [120, 5333, 5351]