{"id":2703,"date":"2016-12-16T06:00:17","date_gmt":"2016-12-16T04:00:17","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2703"},"modified":"2022-03-25T20:18:04","modified_gmt":"2022-03-25T18:18:04","slug":"numeros-de-la-suerte","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-de-la-suerte\/","title":{"rendered":"N\u00fameros de la suerte"},"content":{"rendered":"<p>Un <a href=\"http:\/\/bit.ly\/2gG48Sl\">n\u00famero de la suerte<\/a> es un n\u00famero natural que se genera por una criba, similar a la criba de Erat\u00f3stenes, como se indica a continuaci\u00f3n:<\/p>\n<p>Se comienza con la lista de los n\u00fameros enteros a partir de 1:<\/p>\n<pre lang=\"text\">\n   1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25...\n<\/pre>\n<p>Se eliminan los n\u00fameros de dos en dos<\/p>\n<pre lang=\"text\">\n   1,  3,  5,  7,  9,   11,   13,   15,   17,   19,   21,   23,   25...\n<\/pre>\n<p>Como el segundo n\u00famero que ha quedado es 3, se eliminan los n\u00fameros<br \/>\nrestantes de tres en tres:<\/p>\n<pre lang=\"text\">\n   1,  3,      7,  9,         13,   15,         19,   21,         25...\n<\/pre>\n<p>Como el tercer n\u00famero que ha quedado es 7, se eliminan los n\u00fameros restantes de<br \/>\nsiete en siete:<\/p>\n<pre lang=\"text\">\n   1,  3,      7,  9,         13,   15,               21,         25...\n<\/pre>\n<p>Este procedimiento se repite indefinidamente y los supervivientes son<br \/>\nlos n\u00fameros de la suerte:<\/p>\n<pre lang=\"text\">\n   1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79\n<\/pre>\n<p>Definir la sucesi\u00f3n<\/p>\n<pre lang=\"text\">\n   numerosDeLaSuerte :: [Int]\n<\/pre>\n<p>cuyos elementos son los n\u00fameros de la suerte. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> take 20 numerosDeLaSuerte\n   [1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79]\n   \u03bb> numerosDeLaSuerte !! 1500\n   13995\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n\nnumerosDeLaSuerte :: [Int]\nnumerosDeLaSuerte = criba 3 [1,3..]\n  where\n    criba i (n:s:xs) =\n      n : criba (i + 1) (s : [x | (n, x) <- zip [i..] xs\n                                , rem n s \/= 0])\n\n-- 2\u00aa definici\u00f3n\nnumerosDeLaSuerte2 :: [Int]\nnumerosDeLaSuerte2 =  1 : criba 2 [1, 3..]\n  where criba k xs = z : criba (k + 1) (aux xs)\n          where z = xs !! (k - 1 )\n                aux ws = us ++ aux vs\n                  where (us, _:vs) = splitAt (z - 1) ws \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero de la suerte es un n\u00famero natural que se genera por una criba, similar a la criba de Erat\u00f3stenes, como se indica a continuaci\u00f3n: Se comienza con la lista de los n\u00fameros enteros a partir de 1: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25&#8230; Se eliminan los n\u00fameros de dos en dos 1, 3, 5, 7, 9, 11, 13,&#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":[8,415,6,31,73,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2703"}],"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=2703"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2703\/revisions"}],"predecessor-version":[{"id":2737,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2703\/revisions\/2737"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2703"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2703"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2703"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}