{"id":1169,"date":"2015-03-06T06:00:29","date_gmt":"2015-03-06T04:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1169"},"modified":"2015-03-13T08:40:50","modified_gmt":"2015-03-13T06:40:50","slug":"numeros-con-la-misma-cantidad-de-anteriores-con-1-que-sin-1","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-con-la-misma-cantidad-de-anteriores-con-1-que-sin-1\/","title":{"rendered":"N\u00fameros con la misma cantidad de anteriores con 1 que sin 1"},"content":{"rendered":"<p>Una propiedad del n\u00famero 24 es que entre los n\u00fameros menores o iguales que 24 hay la misma cantidad de n\u00fameros con el d\u00edgito 1 que sin el 1; en efecto, los que tienen 1 son<\/p>\n<pre lang=\"text\">\n   [1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]\n<\/pre>\n<p>y los que no lo tienen son<\/p>\n<pre lang=\"text\">\n   [2,  3,  4,  5,  6,  7,  8,  9, 20, 22, 23, 24]\n<\/pre>\n<p>Diremos que un n\u00famero es especial si cumple dicha propiedad.<\/p>\n<p>Definir la sucesi\u00f3n<\/p>\n<pre lang=\"text\">\n   especiales :: [Integer]\n<\/pre>\n<p>cuyos elementos son los n\u00fameros especiales. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   take 10 especiales  ==  [2,16,24,160,270,272,1456,3398,3418,3420]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (genericLength)\n\nespeciales :: [Integer]\nespeciales = [n | n <- [2,4..], especial n]\n\nespecial :: Integer -> Bool\nespecial n = genericLength [x | x <- [1..n], '1' `elem` show x] == n `div` 2\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Una propiedad del n\u00famero 24 es que entre los n\u00fameros menores o iguales que 24 hay la misma cantidad de n\u00fameros con el d\u00edgito 1 que sin el 1; en efecto, los que tienen 1 son [1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21] y los que no lo tienen son&#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":[5],"tags":[8,30,26,258,33],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1169"}],"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=1169"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1169\/revisions"}],"predecessor-version":[{"id":1202,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1169\/revisions\/1202"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}