{"id":1434,"date":"2015-05-08T07:05:28","date_gmt":"2015-05-08T05:05:28","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1434"},"modified":"2015-06-13T16:32:14","modified_gmt":"2015-06-13T14:32:14","slug":"potencias-de-primos-con-exponentes-potencias-de-dos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/potencias-de-primos-con-exponentes-potencias-de-dos\/","title":{"rendered":"Potencias de primos con exponentes potencias de dos"},"content":{"rendered":"<p>Se llaman potencias de Fermi-Dirac a los n\u00fameros de la forma p^(2^k), donde p es un n\u00famero primo y k es un n\u00famero natural.<\/p>\n<p>Definir la sucesi\u00f3n<\/p>\n<pre lang=\"text\">\n   potencias :: [Integer]\n<\/pre>\n<p>cuyos t\u00e9rminos sean las potencias de Fermi-Dirac ordenadas de menor a mayor. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   take 14 potencias    ==  [2,3,4,5,7,9,11,13,16,17,19,23,25,29]\n   potencias !! 60      ==  241\n   potencias !! (10^6)  ==  15476303\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (primes)\n\npotencias :: [Integer]\npotencias = 2 : mezcla (tail primes) (map (^2) potencias)\n\n-- (mezcla xs ys) es la lista obtenida mezclando las dos listas xs e ys,\n-- que se suponen ordenadas y disjuntas. Por ejemplo,\n--    ghci> take 15 (mezcla [2^n | n <- [1..]] [3^n | n <- [1..]])\n--    [2,3,4,8,9,16,27,32,64,81,128,243,256,512,729]\nmezcla :: Ord a => [a] -> [a] -> [a]\nmezcla (x:xs) (y:ys) | x < y = x : mezcla xs (y:ys)\n                     | x > y = y : mezcla (x:xs) ys\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Se llaman potencias de Fermi-Dirac a los n\u00fameros de la forma p^(2^k), donde p es un n\u00famero primo y k es un n\u00famero natural. Definir la sucesi\u00f3n potencias :: [Integer] cuyos t\u00e9rminos sean las potencias de Fermi-Dirac ordenadas de menor a mayor. Por ejemplo, take 14 potencias == [2,3,4,5,7,9,11,13,16,17,19,23,25,29] potencias !! 60 == 241 potencias&#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":[7],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1434"}],"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=1434"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1434\/revisions"}],"predecessor-version":[{"id":1524,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1434\/revisions\/1524"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1434"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1434"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1434"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}