{"id":6184,"date":"2021-03-17T06:00:26","date_gmt":"2021-03-17T04:00:26","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6184"},"modified":"2021-03-24T09:27:17","modified_gmt":"2021-03-24T07:27:17","slug":"numeros-con-cuadrados-con-digitos-pares","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-con-cuadrados-con-digitos-pares\/","title":{"rendered":"N\u00fameros con cuadrados con d\u00edgitos pares"},"content":{"rendered":"<p>Definir la lista<\/p>\n<pre lang=\"text\">\n   numerosConCuadradosConDigitosPares :: [Integer]\n<\/pre>\n<p>cuyos elementos son los n\u00fameros cuyos cuadrados tienen todos sus d\u00edgitos pares. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> take 20 numerosConCuadradosConDigitosPares\n   [0,2,8,20,22,68,78,80,92,162,168,200,202,220,262,298,478,492,498,668]\n<\/pre>\n<p>Comprobar con QuickCheck que numerosConCuadradosConDigitosPares es infinita; es decir, para cualquier n posee alg\u00fan elemento mayor que n.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nnumerosConCuadradosConDigitosPares :: [Integer]\nnumerosConCuadradosConDigitosPares =\n  filter tieneCuadradoConDigitosPares [0..]\n\n-- (tieneCuadradoConDigitosPares n) se verifica si todos los d\u00edgitos de\n-- n^2 son pares. Por ejemplo,\n--    tieneCuadradoConDigitosPares 78  ==  True\n--    tieneCuadradoConDigitosPares 76  ==  False\ntieneCuadradoConDigitosPares :: Integer -> Bool\ntieneCuadradoConDigitosPares n =\n  tieneDigitosPares (n^2)\n\n-- (tieneDigitosPares n) se verifica si todos los d\u00edgitos de n son\n-- pares. Por ejemplo,\n--    tieneDigitosPares 426  ==  True\n--    tieneDigitosPares 436  ==  False\ntieneDigitosPares :: Integer -> Bool\ntieneDigitosPares n =\n  all even (digitos n)\n\n-- (digitos n) es la lista de los d\u00edgitos de n. Por ejemplo,\n--    digitos 325  ==  [3,2,5]\ndigitos :: Integer -> [Int]\ndigitos n =\n  [read [c] | c <- show n]\n\n-- La propiedad es\nprop_infinito :: Integer -> Bool\nprop_infinito n =\n  not (null (dropWhile (<= n) numerosConCuadradosConDigitosPares))\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_infinito\n--    +++ OK, passed 100 tests.\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Definir la lista numerosConCuadradosConDigitosPares :: [Integer] cuyos elementos son los n\u00fameros cuyos cuadrados tienen todos sus d\u00edgitos pares. Por ejemplo, \u03bb> take 20 numerosConCuadradosConDigitosPares [0,2,8,20,22,68,78,80,92,162,168,200,202,220,262,298,478,492,498,668] Comprobar con QuickCheck que numerosConCuadradosConDigitosPares es infinita; es decir, para cualquier n posee alg\u00fan elemento mayor que n. Soluciones import Test.QuickCheck numerosConCuadradosConDigitosPares :: [Integer] numerosConCuadradosConDigitosPares = filter tieneCuadradoConDigitosPares [0..] &#8211;&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6184"}],"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=6184"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6184\/revisions"}],"predecessor-version":[{"id":6219,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6184\/revisions\/6219"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}