{"id":1745,"date":"2020-08-30T06:45:14","date_gmt":"2020-08-30T06:45:14","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=1745"},"modified":"2020-09-05T07:48:21","modified_gmt":"2020-09-05T07:48:21","slug":"sucesion-recursiva-2","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2020\/08\/30\/sucesion-recursiva-2\/","title":{"rendered":"Sucesi\u00f3n recursiva"},"content":{"rendered":"<pre>Problema 2 de la fase nacional de la 56 Olimpiada Matem\u00e1tica Espa\u00f1ola (2020)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Consideramos la sucesi\u00f3n de n\u00fameros enteros f(n), con n mayor o igual que 1, definida por las siguientes condiciones:<\/p>\n<p>f(1) = 1.<\/p>\n<p>Si n es par, f(n) = f(n\/2).<\/p>\n<p>Si n es impar y f(n \u2013 1) es impar, entonces f(n) = f(n \u2013 1) \u2013 1.<\/p>\n<p>Si n es impar y f(n \u2013 1) es par, entonces f(n) = f(n \u2013 1) + 1.<\/p>\n<p>a) Calcula f(2<sup>2020<\/sup> \u2013 1).<\/p>\n<p>b) Demuestra que la sucesi\u00f3n no es peri\u00f3dica, es decir, que no existen enteros positivos t y n<sub>0<\/sub> que cumplan  que si n es mayor que n<sub>0<\/sub>, entonces f(n + t) = f(n).<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2020\/08\/159.Sucesionrecursiva.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-1746\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2020\/08\/159.Sucesionrecursiva.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2020\/08\/159.Sucesionrecursiva-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2020\/09\/05\/solucion-a-sucesion-recursiva-2\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 2 de la fase nacional de la 56 Olimpiada Matem\u00e1tica Espa\u00f1ola (2020) Se dirige a una edad de: 16-17 a\u00f1os Consideramos la sucesi\u00f3n de n\u00fameros enteros f(n), con n mayor o igual que 1, definida por las siguientes condiciones: f(1) = 1. Si n es par, f(n) = f(n\/2). Si n es impar y [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2849],"tags":[],"class_list":["post-1745","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1745","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=1745"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1745\/revisions"}],"predecessor-version":[{"id":1753,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1745\/revisions\/1753"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=1745"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=1745"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=1745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}