{"id":4500,"date":"2019-01-04T06:00:07","date_gmt":"2019-01-04T04:00:07","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4500"},"modified":"2022-03-25T20:08:04","modified_gmt":"2022-03-25T18:08:04","slug":"el-2019-es-un-numero-de-la-suerte","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/el-2019-es-un-numero-de-la-suerte\/","title":{"rendered":"El 2019 es un n\u00famero de la suerte"},"content":{"rendered":"

Un 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

Se comienza con la lista de los n\u00fameros enteros a partir de 1:<\/p>\n

\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
Se eliminan los n\u00fameros de dos en dos<\/p>\n
\n   1,  3,  5,  7,  9,   11,   13,   15,   17,   19,   21,   23,   25...\n<\/pre>\n
Como el segundo n\u00famero que ha quedado es 3, se eliminan los n\u00fameros restantes de tres en tres:<\/p>\n
\n   1,  3,      7,  9,         13,   15,         19,   21,         25...\n<\/pre>\n
Como el tercer n\u00famero que ha quedado es 7, se eliminan los n\u00fameros restantes de siete en siete:<\/p>\n
\n   1,  3,      7,  9,         13,   15,               21,         25...\n<\/pre>\n
Este procedimiento se repite indefinidamente y los supervivientes son los n\u00fameros de la suerte:<\/p>\n
\n   1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79\n<\/pre>\n
Definir las funciones<\/p>\n
\n   numerosDeLaSuerte  :: [Int]\n   esNumeroDeLaSuerte :: Int -> Bool\n<\/pre>\n
tales que<\/p>\n
    \n
  • numerosDeLaSuerte es la sucesi\u00f3n de los n\u00fameros de la suerte. Por ejemplo, <\/li>\n<\/ul>\n
    \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 !! 277\n     2019\n     \u03bb> numerosDeLaSuerte !! 2000\n     19309\n<\/pre>\n
      \n
    • (esNumeroDeLaSuerte n) que se verifica si n es un n\u00famero de la suerte. Por ejemplo,<\/li>\n<\/ul>\n
      \n   esNumeroDeLaSuerte 15    ==  True\n   esNumeroDeLaSuerte 16    ==  False\n   esNumeroDeLaSuerte 2019  ==  True\n<\/pre>\n
      Soluciones<\/h4>\n
      \n-- 1\u00aa definici\u00f3n de numerosDeLaSuerte \nnumerosDeLaSuerte :: [Int]\nnumerosDeLaSuerte = criba 3 [1,3..]\n  where\n    criba i (n:s:xs) =\n      n : criba (i + 1) (s : [x | (k, x) <- zip [i..] xs\n                                , rem k s \/= 0])\n\n-- 2\u00aa definici\u00f3n de numerosDeLaSuerte \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\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> numerosDeLaSuerte2 !! 200\n--    1387\n--    (9.25 secs, 2,863,983,232 bytes)\n--    \u03bb> numerosDeLaSuerte !! 200\n--    1387\n--    (0.06 secs, 10,263,880 bytes)\n\n-- Definici\u00f3n de esNumeroDeLaSuerte\nesNumeroDeLaSuerte :: Int -> Bool\nesNumeroDeLaSuerte n =\n  n == head (dropWhile (\n
      Pensamiento<\/h4>\n
      \nYa es s\u00f3lo brocal el pozo;
      \np\u00falpito ser\u00e1 ma\u00f1ana;
      \npasado ma\u00f1ana, trono.<\/p>\n
      Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
      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… Se eliminan los n\u00fameros de dos en dos 1, 3, 5, 7, 9, 11, 13,…<\/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":[59,71,415,11,6,31,73,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4500"}],"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=4500"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4500\/revisions"}],"predecessor-version":[{"id":4535,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4500\/revisions\/4535"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}