Potencias de primos con exponentes potencias de dos

4 Comentarios

1. Haskell

   import Data.Bits ((.&.)) import Data.Numbers.Primes (primeFactors) import Data.List (genericLength) potencias :: [Integer] potencias = filter esFermiDirac [2..] esFermiDirac :: Integer -> Bool esFermiDirac p = all (== head xs) xs && esPotenciaDeDos (genericLength xs) where xs = primeFactors p esPotenciaDeDos :: Integer -> Bool esPotenciaDeDos n = n .&. (n-1) == 0

   1 2 3 4 5 6 7 8 9 10 11 12 13

   import Data.Bits ((.&.)) import Data.Numbers.Primes (primeFactors) import Data.List (genericLength)   potencias :: [Integer] potencias = filter esFermiDirac [2..]            esFermiDirac :: Integer -> Bool esFermiDirac p = all (== head xs) xs && esPotenciaDeDos (genericLength xs)     where xs = primeFactors p   esPotenciaDeDos :: Integer -> Bool esPotenciaDeDos n = n .&. (n-1) == 0

   Responder

2. Utilizando la mezcla de infinitas listas infinitas ordenadas:

   Haskell

   import Data.Numbers.Primes (primes) potencias :: [Integer] potencias = mezclaTodas (iterate f primes) where f xs = zipWith (*) xs xs mezcla :: Ord a => [a] -> [a] -> [a] mezcla (x:xs) (y:ys) | x < y = x : mezcla xs (y:ys) | x > y = y : mezcla (x:xs) ys | otherwise = x : mezcla xs ys mezclaTodas :: Ord a => [[a]] -> [a] mezclaTodas = foldr1 xmezcla where xmezcla (x:xs) ys = x : mezcla xs ys

   1 2 3 4 5 6 7 8 9 10 11 12 13 14

   import Data.Numbers.Primes (primes)   potencias :: [Integer] potencias = mezclaTodas (iterate f primes)     where f xs = zipWith (*) xs xs   mezcla :: Ord a => [a] -> [a] -> [a] mezcla (x:xs) (y:ys) | x < y     = x : mezcla xs (y:ys)                      | x > y     = y : mezcla (x:xs) ys                      | otherwise = x : mezcla xs ys                                            mezclaTodas :: Ord a => [[a]] -> [a] mezclaTodas = foldr1 xmezcla     where xmezcla (x:xs) ys = x : mezcla xs ys

   Responder

3. Haskell

   import Data.Numbers.Primes (primes) potencias :: [Integer] potencias = ordena [ [ p^(2^k) | p <- primes ] | k <- [0..] ] where ordena ((x:xs):xss) = x : mezcla xs (ordena xss) mezcla (x:xs) (y:ys) | x <= y = x : mezcla xs (y:ys) | otherwise = y : mezcla (x:xs) ys

   1 2 3 4 5 6 7 8 9

   import Data.Numbers.Primes (primes)   potencias :: [Integer] potencias = ordena [ [ p^(2^k) | p <- primes ] | k <- [0..] ]     where         ordena ((x:xs):xss) = x : mezcla xs (ordena xss)         mezcla (x:xs) (y:ys)             | x <= y    = x : mezcla xs (y:ys)             | otherwise = y : mezcla (x:xs) ys

   Responder

4. Haskell

   import Data.Numbers.Primes potencias :: [Integer] potencias = [x | x <- [2..], (quePoten (dame x) (poten 2) 1) /= 0] dame x = quePoten x (poten (factor x)) 0 factor :: Integer -> Integer factor x = head [s | s <- [2..x], mod x s == 0, isPrime s] quePoten :: Integer -> [Integer] -> Integer -> Integer quePoten x (t:xs) s | x > t = quePoten x xs (s+1) | x == t = s | otherwise = 0 poten :: Integer -> [Integer] poten p = [p^x | x <- [0..]]

   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

   import Data.Numbers.Primes   potencias :: [Integer] potencias = [x | x <- [2..], (quePoten (dame x) (poten 2) 1) /= 0]   dame x = quePoten x (poten (factor x)) 0   factor :: Integer -> Integer factor x = head [s | s <- [2..x], mod x s == 0, isPrime s]   quePoten :: Integer -> [Integer] -> Integer -> Integer quePoten x (t:xs) s | x > t     = quePoten x xs (s+1)                     | x == t    = s                     | otherwise = 0   poten :: Integer -> [Integer] poten p = [p^x | x <- [0..]]

   Responder