{"id":1659,"date":"2015-10-30T06:00:06","date_gmt":"2015-10-30T04:00:06","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1659"},"modified":"2015-11-20T08:05:40","modified_gmt":"2015-11-20T06:05:40","slug":"factoriales-iguales-a-su-numero-de-digitos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/factoriales-iguales-a-su-numero-de-digitos\/","title":{"rendered":"Factoriales iguales a su n\u00famero de d\u00edgitos"},"content":{"rendered":"<p>Se dice que un n\u00famero n tiene un factorial especial si el n\u00famero de d\u00edgitos de n! es igual a n. Por ejemplo, 22 tiene factorial especial porque 22! es 1124000727777607680000 que tiene 22 d\u00edgitos.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   factorialesEspeciales :: [Integer]\n<\/pre>\n<p>tal que su valor es la lista de los n\u00fameros que tienen factoriales especiales. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   take 2 factorialesEspeciales  ==  [1,22]\n<\/pre>\n<p><strong>Nota<\/strong>: Si factorialesEspeciales es una lista finita, argumentar porqu\u00e9 no puede tener m\u00e1s elementos.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (genericLength)\n\nfactorialesEspeciales :: [Integer]\nfactorialesEspeciales =\n    [n | n <- [1..], tieneFactorialEspecial n]\n\ntieneFactorialEspecial :: Integer -> Bool\ntieneFactorialEspecial n = n == genericLength (show (factorial n))\n\nfactorial :: Integer -> Integer\nfactorial n = product [1..n]\n\n-- El c\u00e1lculo es\n--    ghci> factorialesEspeciales\n--    [1,22,23,24  C-c C-cInterrupted.\n\n-- Para comprobar que no hay m\u00e1s definimos\n\ncrecimiento :: [(Integer,Integer)]\ncrecimiento = [(n,n - genericLength (show (factorial n))) | n <- [1..]]\n\n-- Al evaluarla\n\n--    ghci> take 30 crecimiento \n--    [(1,0),(2,1),(3,2),(4,2),(5,2),(6,3),(7,3),(8,3),(9,3),(10,3),(11,3),\n--     (12,3),(13,3),(14,3),(15,2),(16,2),(17,2),(18,2),(19,1),(20,1),(21,1),\n--     (22,0),(23,0),(24,0),(25,-1),(26,-1),(27,-2),(28,-2),(29,-2),(30,-3)]\n\n-- se observa que, a partir de n = 25, el n\u00famero de cifras del factorial\n-- de n es mayor que n. \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Se dice que un n\u00famero n tiene un factorial especial si el n\u00famero de d\u00edgitos de n! es igual a n. Por ejemplo, 22 tiene factorial especial porque 22! es 1124000727777607680000 que tiene 22 d\u00edgitos. Definir la funci\u00f3n factorialesEspeciales :: [Integer] tal que su valor es la lista de los n\u00fameros que tienen factoriales especiales&#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":[4],"tags":[8,258,33],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1659"}],"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=1659"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1659\/revisions"}],"predecessor-version":[{"id":1750,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1659\/revisions\/1750"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}