{"id":1412,"date":"2015-05-04T06:00:12","date_gmt":"2015-05-04T04:00:12","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1412"},"modified":"2022-03-25T20:22:32","modified_gmt":"2022-03-25T18:22:32","slug":"numeros-cuyas-cifras-coinciden-con-las-de-sus-factores-primos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-cuyas-cifras-coinciden-con-las-de-sus-factores-primos\/","title":{"rendered":"N\u00fameros cuyas cifras coinciden con las de sus factores primos"},"content":{"rendered":"<p>Un n\u00famero n es especial si al unir las cifras de sus factores primos, se obtienen exactamente las cifras de n, aunque puede ser en otro orden. Por ejemplo, 1255 es especial, pues los factores primos de 1255 son 5 y 251.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esEspecial :: Integer -> Bool\n<\/pre>\n<p>tal que (esEspecial n) se verifica si un n\u00famero n es especial. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   esEspecial 1255 == True\n   esEspecial 125  == False\n<\/pre>\n<p>Comprobar con QuickCheck que todo n\u00famero primo es especial.<\/p>\n<p>Calcular los 5 primeros n\u00fameros especiales que no son primos.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (nub, sort)\nimport Data.Numbers.Primes (isPrime, primeFactors)\nimport Test.QuickCheck\n\nesEspecial :: Integer -> Bool\nesEspecial n = \n    sort (show n) == sort (concatMap show (nub (primeFactors n)))\n\n-- La propiedad es\nprop_primos:: Integer -> Property\nprop_primos n = \n    isPrime (abs n) ==> esEspecial (abs n)\n\n-- La comprobaci\u00f3n es\n--    ghci> quickCheck prop_primos\n--    +++ OK, passed 100 tests.\n\n-- El c\u00e1lculo es\n--    ghci> take 5 [n | n <- [2..], esEspecial n, not (isPrime n)]\n--    [735,1255,3792,7236,11913]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero n es especial si al unir las cifras de sus factores primos, se obtienen exactamente las cifras de n, aunque puede ser en otro orden. Por ejemplo, 1255 es especial, pues los factores primos de 1255 son 5 y 251. Definir la funci\u00f3n esEspecial :: Integer -> Bool tal que (esEspecial n) se&#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":[130,58,174,415,181,24,11,247,33,14,47,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1412"}],"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=1412"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1412\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1412\/revisions\/1443"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}