{"id":5941,"date":"2020-06-01T07:34:55","date_gmt":"2020-06-01T05:34:55","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5941"},"modified":"2021-01-02T22:34:07","modified_gmt":"2021-01-02T20:34:07","slug":"la-sucesion-ecg","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/la-sucesion-ecg\/","title":{"rendered":"La sucesi\u00f3n ECG"},"content":{"rendered":"<p>La sucesi\u00f3n ECG est\u00e1s definida por a(1) = 1, a(2) = 2 y, para n >= 3, a(n) es el menor natural que a\u00fan no est\u00e1 en la sucesi\u00f3n tal que a(n) tiene alg\u00fan divisor com\u00fan con a(n-1).<\/p>\n<p>Los primeros t\u00e9rminos de la sucesi\u00f3n son 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, &#8230;<\/p>\n<p>Al dibujar su gr\u00e1fica, se parece a la de los electrocardiogramas (abreviadamente, ECG). Por ello, la sucesi\u00f3n se conoce como la sucesi\u00f3n ECG.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\"> \n   sucECG :: [Integer]\n   graficaSucECG :: Int -> IO ()\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>sucECG es la lista de los t\u00e9rminos de la sucesi\u00f3n ECG. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\"> \n     \u03bb> take 20 sucECG\n     [1,2,4,6,3,9,12,8,10,5,15,18,14,7,21,24,16,20,22,11]\n     \u03bb> sucECG !! 6000\n     6237\n<\/pre>\n<ul>\n<li>(graficaSucECG n) dibuja la gr\u00e1fica de los n primeros t\u00e9rminos de la sucesi\u00f3n ECG. Por ejemplo, (graficaSucECG 160) dibuja<\/li>\n<\/ul>\n<p><a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/La_sucesion_ECG.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/La_sucesion_ECG.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4850\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/La_sucesion_ECG.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/La_sucesion_ECG.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (delete)\nimport Graphics.Gnuplot.Simple\n\nsucECG :: [Integer]\nsucECG = 1 : ecg 2 [2..]\n  where ecg x zs = f zs\n          where f (y:ys) | gcd x y > 1 = y : ecg y (delete y zs)\n                         | otherwise   = f ys\n\ngraficaSucECG :: Int -> IO ()\ngraficaSucECG n =\n  plotList [ Key Nothing\n           , PNG \"La_sucesion_ECG.png\" \n           ]\n           (take n sucECG)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>La sucesi\u00f3n ECG est\u00e1s definida por a(1) = 1, a(2) = 2 y, para n >= 3, a(n) es el menor natural que a\u00fan no est\u00e1 en la sucesi\u00f3n tal que a(n) tiene alg\u00fan divisor com\u00fan con a(n-1). Los primeros t\u00e9rminos de la sucesi\u00f3n son 1, 2, 4, 6, 3, 9, 12, 8, 10, 5,&#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":[4],"tags":[25,155,376,309,6,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5941"}],"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=5941"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5941\/revisions"}],"predecessor-version":[{"id":5968,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5941\/revisions\/5968"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}