{"id":2304,"date":"2016-04-11T06:00:20","date_gmt":"2016-04-11T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2304"},"modified":"2016-04-18T08:27:43","modified_gmt":"2016-04-18T06:27:43","slug":"primos-permutables","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/primos-permutables\/","title":{"rendered":"Primos permutables"},"content":{"rendered":"<p>Un <a href=\"http:\/\/bit.ly\/1N2wuFs\">primo permutable<\/a> es un n\u00famero primo tal que todos los n\u00fameros obtenidos permutando sus cifras son primos. Por ejemplo, 337 es un primo permutable ya que 337, 373 y 733 son primos.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   esPrimoPermutable :: Integer -> Bool\n   primosPermutables :: [Integer]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(esPrimoPermutable x) se verifica si x es un primo permutable. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     esPrimoPermutable 97  ==  True\n     esPrimoPermutable 337 ==  True\n     esPrimoPermutable 23  ==  False\n<\/pre>\n<ul>\n<li>primosPermutables es la lista de los primos permutables. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> take 20 primosPermutables\n     [2,3,5,7,11,13,17,31,37,71,73,79,97,113,131,199,311,337,373,733]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (nub, permutations)\nimport Data.Numbers.Primes (primes, isPrime)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n    \nesPrimoPermutable :: Integer -> Bool\nesPrimoPermutable x =\n    all isPrime (permutacionesN x)\n\npermutacionesN :: Integer -> [Integer]\npermutacionesN x =\n    [read ys | ys <- nub (permutations xs)]\n    where xs = show x\n          n  = length xs\n        \nprimosPermutables :: [Integer]\nprimosPermutables =\n    [x | x <- primes, esPrimoPermutable x]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nesPrimoPermutable2 :: Integer -> Bool\nesPrimoPermutable2 = all isPrime . map read . nub . permutations . show\n \nprimosPermutables2 :: [Integer]\nprimosPermutables2 = filter esPrimoPermutable2 primes\n<\/pre>\n<h4>Referencias<\/h4>\n<ul>\n<li><a href=\"http:\/\/bit.ly\/1N2wuFs\">Permutable prime<\/a> en Wikipedia.<\/li>\n<li><a href=\"https:\/\/oeis.org\/A003459\">Sucesi\u00f3n A003459<\/a> de la OEIS.\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Un primo permutable es un n\u00famero primo tal que todos los n\u00fameros obtenidos permutando sus cifras son primos. Por ejemplo, 337 es un primo permutable ya que 337, 373 y 733 son primos. Definir las funciones esPrimoPermutable :: Integer -> Bool primosPermutables :: [Integer] tales que (esPrimoPermutable x) se verifica si x es un primo&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[5],"tags":[41,8,174,28,24,11,228,173,95,33],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2304"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=2304"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2304\/revisions"}],"predecessor-version":[{"id":2337,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2304\/revisions\/2337"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}