{"id":2591,"date":"2016-11-17T06:00:45","date_gmt":"2016-11-17T04:00:45","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2591"},"modified":"2016-11-24T07:29:19","modified_gmt":"2016-11-24T05:29:19","slug":"numeros-poderosos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-poderosos\/","title":{"rendered":"N\u00fameros poderosos"},"content":{"rendered":"<p>Un n\u00famero es <strong>poderoso<\/strong> si es igual a la suma de sus d\u00edgitos elevados a sus respectivas posiciones. Por ejemplo, los n\u00fameros 89, 135 y 1306 son poderosos ya que<\/p>\n<pre lang=\"text\"> \n     89 = 8^1 + 9^2\n    135 = 1^1 + 3^2 + 5^3.\n   1306 = 1^1 + 3^2 + 0^3 + 6^4\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\"> \n   esPoderoso :: Integer -> Bool\n<\/pre>\n<p>tal que (esPoderoso n) se verifica si n es poderoso. Por ejemplo,<\/p>\n<pre lang=\"text\"> \n   \u03bb> esPoderoso 135\n   True\n   \u03bb> esPoderoso 80\n   False\n   \u03bb> esPoderoso 89\n   True\n   \u03bb> esPoderoso 12157692622039623539\n   True\n   \u03bb> [n | n <- [10..30000], esPoderoso n]\n   [89,135,175,518,598,1306,1676,2427]\n<\/pre>\n<p>Comprobar con QuickCheck que 12157692622039623539 es el mayor n\u00famero poderoso.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nesPoderoso :: Integer -> Bool\nesPoderoso n =\n  sum (zipWith (^) (digitos n) [1..]) == n\n\ndigitos :: Integer -> [Integer]\ndigitos n =\n  [read [d] | d <- show n]\n\n-- La propiedad es\nprop_poderosos :: Integer -> Property\nprop_poderosos n =\n  n > 0 ==> not (esPoderoso (12157692622039623539 + n))\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_poderosos\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero es poderoso si es igual a la suma de sus d\u00edgitos elevados a sus respectivas posiciones. Por ejemplo, los n\u00fameros 89, 135 y 1306 son poderosos ya que 89 = 8^1 + 9^2 135 = 1^1 + 3^2 + 5^3. 1306 = 1^1 + 3^2 + 0^3 + 6^4 Definir la funci\u00f3n esPoderoso&#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":[8,11,95,33,40,76],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2591"}],"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=2591"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2591\/revisions"}],"predecessor-version":[{"id":2614,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2591\/revisions\/2614"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2591"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2591"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2591"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}