{"id":4435,"date":"2018-12-18T06:00:33","date_gmt":"2018-12-18T04:00:33","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4435"},"modified":"2018-12-25T08:46:26","modified_gmt":"2018-12-25T06:46:26","slug":"numeros-primos-de-pierpont","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-primos-de-pierpont\/","title":{"rendered":"N\u00fameros primos de Pierpont"},"content":{"rendered":"<p>Un <a href=\"http:\/\/bit.ly\/2QSizbM\">n\u00famero primo de Pierpont<\/a>  es un n\u00famero primo de la forma <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=2%5E%7Bu%7D3%5E%7Bv%7D%2B1&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"2^{u}3^{v}+1\" class=\"latex\" \/>, para u y v enteros no negativos.<\/p>\n<p>Definir la sucesi\u00f3n<\/p>\n<pre lang=\"text\">\n   primosPierpont :: [Integer]\n<\/pre>\n<p>tal que sus elementos son los n\u00fameros primos de Pierpont. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> take 20 primosPierpont\n   [2,3,5,7,13,17,19,37,73,97,109,163,193,257,433,487,577,769,1153,1297]\n   \u03bb> primosPierpont !! 49\n   8503057\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (primes, primeFactors)\n\nprimosPierpont :: [Integer]\nprimosPierpont =\n  [n | n <- primes\n     , primoPierpont n]\n\nprimoPierpont :: Integer -> Bool\nprimoPierpont n =\n  primeFactors (n-1) `contenidoEn` [2,3]\n\n-- (contenidoEn xs ys) se verifica si xs est\u00e1 contenido en ys. Por\n-- ejemplo,\n--    contenidoEn [2,3,2,2,3] [2,3]  ==  True\n--    contenidoEn [2,3,2,2,1] [2,3]  ==  False\ncontenidoEn :: [Integer] -> [Integer] -> Bool\ncontenidoEn xs ys =\n  all (`elem` ys) xs\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\n\u00abLa memoria es infiel: no s\u00f3lo borra y confunde, sino que, a veces, inventa, para desorientarnos.\u00bb<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero primo de Pierpont es un n\u00famero primo de la forma , para u y v enteros no negativos. Definir la sucesi\u00f3n primosPierpont :: [Integer] tal que sus elementos son los n\u00fameros primos de Pierpont. Por ejemplo, \u03bb> take 20 primosPierpont [2,3,5,7,13,17,19,37,73,97,109,163,193,257,433,487,577,769,1153,1297] \u03bb> primosPierpont !! 49 8503057 Soluciones import Data.Numbers.Primes (primes, primeFactors) primosPierpont ::&#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":[41,8,26,11,247,173],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4435"}],"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=4435"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4435\/revisions"}],"predecessor-version":[{"id":4478,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4435\/revisions\/4478"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}