{"id":5919,"date":"2020-05-25T06:34:37","date_gmt":"2020-05-25T04:34:37","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5919"},"modified":"2020-06-01T07:41:16","modified_gmt":"2020-06-01T05:41:16","slug":"cadenas-de-primos-complementarios","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/cadenas-de-primos-complementarios\/","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<pre lang=\"haskell\">\n\nimport Data.Numbers.Primes\n\n-- (complemento x) es le complemento de x. Por ejemplo,\n--    complemento 1448  == 552\n--    complemento  639  == 561\n--    complemento    7  == 7\ncomplemento :: Integer -> Integer\ncomplemento x = (div x c)*c - (rem x c)\n  where c = 10^(length (show x) - 1)          \n\ncadena :: Integer -> [Integer]\ncadena x    \n  | x < 10 &#038;&#038; isPrime x = [x]\n  | otherwise           = takeWhile isPrime (iterate f x)\n  where f x | x < 10 &#038;&#038; isPrime x = 0\n            | otherwise           = complemento x\n\nconCadena :: Int -> [Integer]\nconCadena n =\n  [y | y <- primes, length (cadena y) == n]\n<\/pre>\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":[5],"tags":[8,30,174,50,28,11,31,33,34],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5919"}],"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=5919"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5919\/revisions"}],"predecessor-version":[{"id":5943,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5919\/revisions\/5943"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}