Números poderosos

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1. Haskell

   import Test.QuickCheck esPoderoso :: Integer -> Bool esPoderoso n = n == sum (zipWith (^) (digitos n) [1..]) digitos :: Integer -> [Integer] digitos n = [read [c] | c <- show n] prop_poderosos :: Positive Integer -> Bool prop_poderosos (Positive n) = (not.esPoderoso) (n + 12157692622039623539)

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   import Test.QuickCheck   esPoderoso :: Integer -> Bool esPoderoso n = n == sum (zipWith (^) (digitos n) [1..])   digitos :: Integer -> [Integer] digitos n = [read [c] | c <- show n]   prop_poderosos :: Positive Integer -> Bool prop_poderosos (Positive n) =   (not.esPoderoso) (n + 12157692622039623539)

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2. Haskell

   import Test.QuickCheck esPoderoso :: Integer -> Bool esPoderoso n = n == sum [x^k | (x,k) <- zip (map (read) [[x] | x <- show n]) [1..]] prop_poderosos :: Integer -> Property prop_poderosos n = n > 0 ==> all (not.esPoderoso) [(x+1)..(x+n)] where x = 12157692622039623539

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   import Test.QuickCheck   esPoderoso :: Integer -> Bool esPoderoso n = n == sum [x^k | (x,k) <- zip (map (read) [[x] | x <- show n])                           [1..]]   prop_poderosos :: Integer -> Property prop_poderosos n = n > 0 ==> all (not.esPoderoso) [(x+1)..(x+n)] where x = 12157692622039623539

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3. Haskell

   esPoderoso :: Integer -> Bool esPoderoso n = n == sum [(read([xs!!a]))^(a+1) | let xs = show n , a <- [0..length xs - 1] ] prop_esPoderoso :: Integer -> Property prop_esPoderoso n = n > 0 && esPoderoso n ==> n < 12157692622039623539 -- Comprobación: -- *Main> quickCheck prop_esPoderoso -- *** Gave up! Passed only 98 tests. prop_esPoderoso2 :: Integer -> Property prop_esPoderoso2 n = n > 12157692622039623539 ==> esPoderoso n == False -- Comprobación -- *Main> quickCheck prop_esPoderoso2 -- *** Gave up! Passed only 0 tests.

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   esPoderoso :: Integer -> Bool esPoderoso n =   n == sum [(read([xs!!a]))^(a+1) | let xs = show n                                   , a <- [0..length xs - 1] ]   prop_esPoderoso :: Integer -> Property prop_esPoderoso n =   n > 0 && esPoderoso n ==> n < 12157692622039623539   -- Comprobación: --    *Main> quickCheck prop_esPoderoso --    *** Gave up! Passed only 98 tests.   prop_esPoderoso2 :: Integer -> Property prop_esPoderoso2 n =   n > 12157692622039623539 ==> esPoderoso n == False   -- Comprobación --    *Main> quickCheck prop_esPoderoso2 --    *** Gave up! Passed only 0 tests.

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   1. Haskell

      prop_esPoderoso3 :: Integer -> Property prop_esPoderoso3 n = n > 1 ==> not (esPoderoso (12157692622039623539*n)) -- *Main> quickCheck prop_esPoderoso3 -- +++ OK, passed 100 tests.

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      prop_esPoderoso3 :: Integer -> Property prop_esPoderoso3 n =    n > 1 ==> not (esPoderoso (12157692622039623539*n))   -- *Main> quickCheck prop_esPoderoso3 -- +++ OK, passed 100 tests.

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