{"id":3240,"date":"2017-04-19T06:00:54","date_gmt":"2017-04-19T04:00:54","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3240"},"modified":"2021-04-25T16:12:10","modified_gmt":"2021-04-25T14:12:10","slug":"numeros-como-sumas-de-primos-consecutivos-2017","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-como-sumas-de-primos-consecutivos-2017\/","title":{"rendered":"N\u00fameros como sumas de primos consecutivos"},"content":{"rendered":"<p>El n\u00famero 311 se puede escribir de 5 formas distintas como suma de 1 o m\u00e1s primos consecutivos<\/p>\n<pre lang=\"text\">\n   311 =  11 +  13 +  17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47\n   311 =  31 +  37 +  41 + 43 + 47 + 53 + 59\n   311 =  53 +  59 +  61 + 67 + 71\n   311 = 101 + 103 + 107\n   311 = 311\n<\/pre>\n<p>el n\u00famero 41 se puede escribir de 4 formas<\/p>\n<pre lang=\"text\">\n   41 =  2 +  3 +  5 + 7 + 11 + 13\n   41 = 11 + 13 + 17\n   41 = 41\n<\/pre>\n<p>y el n\u00famero 14 no se puede escribir como suma de primos consecutivos.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumas :: Integer -> [[Integer]]\n<\/pre>\n<p>tal que (sumas x) es la lista de las formas de escribir x como suma de uno o m\u00e1s n\u00fameros primos consecutivos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> sumas 311\n   [[11,13,17,19,23,29,31,37,41,43,47],[31,37,41,43,47,53,59],\n    [53,59,61,67,71],[101,103,107],[311]]\n   \u03bb> sumas 41\n   [[2,3,5,7,11,13],[11,13,17],[41]]\n   \u03bb> sumas 14\n   []\n   \u03bb> [length (sumas n) | n <- [0..20]]\n   [0,0,1,1,0,2,0,1,1,0,1,1,1,1,0,1,0,2,1,1,0]\n   \u03bb> maximum [length (sumas n) | n <- [1..600]]\n   5\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (primes)\nimport Data.List (span)\n\nsumas :: Integer -> [[Integer]]\nsumas x = [ys | n <- takeWhile (<= x) primes, \n                let ys = sumaDesde x n,\n                not (null ys)]\n\n-- (sumaDesde x n) es la lista de al menos dos n\u00fameros primos\n-- consecutivos a partir del n\u00famero primo n cuya suma es x, si existen y\n-- la lista vac\u00eda en caso contrario. Por ejemplo,\n--    sumaDesde 15 3  ==  [3,5,7]\n--    sumaDesde  7 3  ==  []\nsumaDesde :: Integer -> Integer -> [Integer]\nsumaDesde x n | x == y    = take (1 + length us) ys\n              | otherwise = []\n    where ys       = dropWhile (<n) primes\n          (us,y:_) = span (<x) (scanl1 (+) ys)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El n\u00famero 311 se puede escribir de 5 formas distintas como suma de 1 o m\u00e1s primos consecutivos 311 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 311 = 31 + 37 + 41 + 43 + 47 + 53 +&#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":[8,28,181,141,11,173,252,60,47,34],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3240"}],"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=3240"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3240\/revisions"}],"predecessor-version":[{"id":3273,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3240\/revisions\/3273"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}