{"id":2503,"date":"2016-05-30T09:53:21","date_gmt":"2016-05-30T07:53:21","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2503"},"modified":"2021-04-25T16:25:51","modified_gmt":"2021-04-25T14:25:51","slug":"cadenas-de-primos-complementarios-2016","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/cadenas-de-primos-complementarios-2016\/","title":{"rendered":"Cadenas de primos complementarios"},"content":{"rendered":"<p>El complemento de un n\u00famero positivo x se calcula por el siguiente  procedimiento:<\/p>\n<ul>\n<li>si x es mayor que 9, se toma cada d\u00edgito por su valor posicional y se resta del mayor los otro d\u00edgitos. Por ejemplo, el complemento de 1448 es 1000 &#8211; 400 &#8211; 40 &#8211; 8 = 552. Para  <\/li>\n<li>si x es menor que 10, su complemento es x.<\/li>\n<\/ul>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   cadena    :: Integer -> [Integer]\n   conCadena :: Int -> [Integer]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(cadena x) es la cadena de primos a partir de x tal que cada uno es el complemento del anterior. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     cadena 8         == []\n     cadena 7         == [7]\n     cadena 13        == [13,7]\n     cadena 643       == [643,557,443]\n     cadena 18127     == [18127,1873,127,73,67,53,47]\n     cadena 18181213  == [18181213,1818787,181213,18787,1213,787,613,587]\n<\/pre>\n<ul>\n<li>(conCadena n) es la lista de n\u00fameros cuyas cadenas tienen n elementos. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     take 6 (conCadena 3)                == [23,31,61,67,103,307]\n     [head (conCadena n) | n <- [4..8]]  == [37,43,157,18127,181873]\n<\/pre>\n<h4>Soluciones<\/h4>\n<p>[schedule expon='2016-06-06' expat=\"06:00\"]<\/p>\n<ul>\n<li>Las soluciones se pueden escribir en los comentarios hasta el 06 de junio.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=\"haskell\"&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n<p>[\/schedule]<\/p>\n<p>[schedule on='2016-06-06' at=\"06:00\"]<\/p>\n<pre lang=\"haskell\">\r\nimport Data.Numbers.Primes\r\n\r\ncadena :: Integer -> [Integer]\r\ncadena x    \r\n    | x < 10 &#038;&#038; isPrime x = [x]\r\n    | otherwise           = takeWhile isPrime (iterate f x)\r\n    where f x | x < 10 &#038;&#038; isPrime x = 0\r\n              | otherwise           = complemento x\r\n\r\ncomplemento :: Integer -> Integer\r\ncomplemento x = (div x c)*c - (rem x c)\r\n    where c = 10^(length (show x) - 1)          \r\n\r\nconCadena :: Int -> [Integer]\r\nconCadena n =\r\n    [y | y <- primes, length (cadena y) == n]\r\n<\/pre>\n<p>[\/schedule]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>El complemento de un n\u00famero positivo x se calcula por el siguiente procedimiento: si x es mayor que 9, se toma cada d\u00edgito por su valor posicional y se resta del mayor los otro d\u00edgitos. Por ejemplo, el complemento de 1448 es 1000 &#8211; 400 &#8211; 40 &#8211; 8 = 552. Para si x es&#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":[2],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2503"}],"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=2503"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2503\/revisions"}],"predecessor-version":[{"id":2509,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2503\/revisions\/2509"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}