{"id":1789,"date":"2015-12-04T06:00:03","date_gmt":"2015-12-04T04:00:03","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1789"},"modified":"2015-12-11T08:00:07","modified_gmt":"2015-12-11T06:00:07","slug":"los-numeros-de-smith","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/los-numeros-de-smith\/","title":{"rendered":"Los n\u00fameros de Smith"},"content":{"rendered":"<p>Un <a href=\"http:\/\/bit.ly\/1Ii4Cuy\">n\u00famero de Smith<\/a> es un n\u00famero natural compuesto que cumple que la suma de sus d\u00edgitos es igual a la suma de los d\u00edgitos de todos sus factores primos (si tenemos alg\u00fan factor primo repetido lo sumamos tantas veces como aparezca). Por ejemplo,  el 22 es un n\u00famero de Smith ya que<\/p>\n<pre lang=\"text\">\n    22 = 2*11 y\n   2+2 = 2+(1+1) \n<\/pre>\n<p>y el 4937775 tambi\u00e9n lo es ya que<\/p>\n<pre lang=\"text\">\n   4937775       = 3*5*5*65837 y \n   4+9+3+7+7+7+5 = 3+5+5+(6+5+8+3+7)\n<\/pre>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   esSmith :: Integer -> Bool\n   smith :: [Integer]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(esSmith x) se verifica si x es un n\u00famero de Smith. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     esSmith 22          ==  True\n     esSmith 29          ==  False\n     esSmith 2015        ==  False\n     esSmith 4937775     ==  True\n     esSmith 4567597056  ==  True\n<\/pre>\n<ul>\n<li>smith es la lista cuyos elementos son los n\u00fameros de Smith. Por ejemplo,  <\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> take 17 smith\n     [4,22,27,58,85,94,121,166,202,265,274,319,346,355,378,382,391]\n     \u03bb> smith !! 2000\n     62158\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes\n\nesSmith :: Integer -> Bool\nesSmith x = \n    not (isPrime x) && \n    sumaDigitos x == sum (map sumaDigitos (primeFactors x))\n\nsumaDigitos :: Integer -> Integer\nsumaDigitos x | x < 10 = x\n              | otherwise = x `mod` 10 + sumaDigitos (x `div` 10)\n\nsmith :: [Integer]\nsmith = [x | x <- [1..], esSmith x]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero de Smith es un n\u00famero natural compuesto que cumple que la suma de sus d\u00edgitos es igual a la suma de los d\u00edgitos de todos sus factores primos (si tenemos alg\u00fan factor primo repetido lo sumamos tantas veces como aparezca). Por ejemplo, el 22 es un n\u00famero de Smith ya que 22 =&#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":[8,30,174,10,89,11,247,6,40],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1789"}],"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=1789"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1789\/revisions"}],"predecessor-version":[{"id":1856,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1789\/revisions\/1856"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}