{"id":2004,"date":"2016-01-22T06:00:16","date_gmt":"2016-01-22T04:00:16","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2004"},"modified":"2016-05-01T19:57:03","modified_gmt":"2016-05-01T17:57:03","slug":"sumas-digitales-de-primos-consecutivos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sumas-digitales-de-primos-consecutivos\/","title":{"rendered":"Sumas digitales de primos consecutivos"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   primosConsecutivosConSumasDigitalesPrimas :: Int -> [[Integer]]\n<\/pre>\n<p>tal que (primosConsecutivosConSumasDigitalesPrimas k) es la sucesi\u00f3n de listas de k primos consecutivos tales que las sumas ordenadas de sus d\u00edgitos tambi\u00e9n son primos consecutivos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> take 5 (primosConsecutivosConSumasDigitalesPrimas 2)\n   [[2,3],[3,5],[5,7],[41,43],[43,47]]\n   \u03bb> take 5 (primosConsecutivosConSumasDigitalesPrimas 3)\n   [[2,3,5],[3,5,7],[41,43,47],[191,193,197],[193,197,199]]\n   \u03bb> take 4 (primosConsecutivosConSumasDigitalesPrimas 4)\n   [[2,3,5,7],[3,5,7,11],[191,193,197,199],[821,823,827,829]]\n   \u03bb> primosConsecutivosConSumasDigitalesPrimas 4 !! 50\n   [129197,129209,129221,129223]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Char (digitToInt)\nimport Data.List (isPrefixOf, sort, tails)\nimport Data.Numbers.Primes\n\nprimosConsecutivosConSumasDigitalesPrimas :: Int -> [[Integer]]\nprimosConsecutivosConSumasDigitalesPrimas k = \n    [xs | xs <- map (take k) (tails primes),\n          primosConsecutivos (sort (map sumaDigital xs))]\n\n-- (digitos n) es la lista de los d\u00edgitos de n. Por ejemplo,\n--    digitos 325  ==  [3,2,5]\ndigitos :: Integer -> [Integer]\ndigitos n = [read [d] | d <- show n]\n\n-- (sumaDigital n) es la suma de los d\u00edgitos de n. Por ejemplo, \n--    sumaDigital 325  ==  10\nsumaDigital :: Integer -> Integer\nsumaDigital = sum . digitos\n\n-- (primosConsecutivos xs) se verifica si xs es una lista de primos\n-- consecutivos. Por ejemplo,\n--    primosConsecutivos [5,7,11]  ==  True\n--    primosConsecutivos [5,7,17]  ==  False\nprimosConsecutivos :: [Integer] -> Bool\nprimosConsecutivos (x:xs) =\n    isPrefixOf (x:xs) (dropWhile (<x) primes)\n<\/pre>\n<h4>Referencias<\/h4>\n<p>Basado en el art\u00edculo <a href=\"http:\/\/bit.ly\/1Oqxm3Z\">DigitSums of some consecutive primes<\/a> del blog <a href=\"http:\/\/bit.ly\/1nre1Xr\">Fun With Num3ers<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n primosConsecutivosConSumasDigitalesPrimas :: Int -> [[Integer]] tal que (primosConsecutivosConSumasDigitalesPrimas k) es la sucesi\u00f3n de listas de k primos consecutivos tales que las sumas ordenadas de sus d\u00edgitos tambi\u00e9n son primos consecutivos. Por ejemplo, \u03bb> take 5 (primosConsecutivosConSumasDigitalesPrimas 2) [[2,3],[3,5],[5,7],[41,43],[43,47]] \u03bb> take 5 (primosConsecutivosConSumasDigitalesPrimas 3) [[2,3,5],[3,5,7],[41,43,47],[191,193,197],[193,197,199]] \u03bb> take 4 (primosConsecutivosConSumasDigitalesPrimas 4) [[2,3,5,7],[3,5,7,11],[191,193,197,199],[821,823,827,829]] \u03bb> primosConsecutivosConSumasDigitalesPrimas&#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":[7],"tags":[8,59,170,10,11,173,95,33,14,40,75,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2004"}],"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=2004"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2004\/revisions"}],"predecessor-version":[{"id":2060,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2004\/revisions\/2060"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}