{"id":2195,"date":"2016-03-03T06:00:36","date_gmt":"2016-03-03T04:00:36","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2195"},"modified":"2016-03-10T06:57:27","modified_gmt":"2016-03-10T04:57:27","slug":"numeros-n-cuyos-cuadrados-tienen-dos-copias-de-cada-digito-de-n","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-n-cuyos-cuadrados-tienen-dos-copias-de-cada-digito-de-n\/","title":{"rendered":"N\u00fameros N cuyos cuadrados tienen dos copias de cada d\u00edgito de N"},"content":{"rendered":"<p>La <a href=\"https:\/\/oeis.org\/A114258\">sucesi\u00f3n A114258 de la OEIS<\/a> est\u00e1 formada por los n\u00fameros n tales que el n\u00famero de ocurrencia de cada d\u00edgito d de n en n\u00b2 es el doble del n\u00famero de ocurrencia de d en n. Por ejemplo, 72576 es un elemento de A114258 porque tiene un 2, un 5, un 6 y dos 7 y su cuadrado es 5267275776 que tiene exactamente dos 2, dos 5, dos 6 y cuatro 7.<\/p>\n<p>Un n\u00famero es especial si pertenece a la sucesi\u00f3n A114258.<\/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 5 especiales  ==  [72576,406512,415278,494462,603297]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (sort)\n\nespeciales :: [Integer]\nespeciales = filter especial [1..]\n\nespecial :: Integer -> Bool\nespecial x = sort (ys ++ ys) == sort (show (x^2))\n    where ys = show x\n<\/pre>\n<h4>En Maxima<\/h4>\n<pre lang=\"text\">\nespeciales (n) := block ([k:0, r:[], i:1],\n  while k < n do\n    ( if especial (i)\n      then (r : cons (i,r), k : k+1),\n      i : i+1),\n  reverse (r))$\n  \nespecial (n) := block([ys],\n  ys : string(n),\n  is (ssort (sconcat(ys,ys)) = ssort (string (n^2))))$\n\n\/*\n   (%i15) showtime : true$\n   Evaluation took 0.0000 seconds (0.0000 elapsed)\n   (%i16) especiales (5);\n   Evaluation took 29.4800 seconds (29.5400 elapsed)\n   (%o16) [72576, 406512, 415278, 494462, 603297]\n*\/\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>La sucesi\u00f3n A114258 de la OEIS est\u00e1 formada por los n\u00fameros n tales que el n\u00famero de ocurrencia de cada d\u00edgito d de n en n\u00b2 es el doble del n\u00famero de ocurrencia de d en n. Por ejemplo, 72576 es un elemento de A114258 porque tiene un 2, un 5, un 6 y dos&#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":[38,11,33,14],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2195"}],"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=2195"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2195\/revisions"}],"predecessor-version":[{"id":2219,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2195\/revisions\/2219"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}