{"id":1550,"date":"2008-06-05T07:02:22","date_gmt":"2008-06-05T05:02:22","guid":{"rendered":"http:\/\/www.randform.org\/blog\/?p=1550"},"modified":"2008-06-05T07:02:22","modified_gmt":"2008-06-05T05:02:22","slug":"collatz-conjecture","status":"publish","type":"post","link":"https:\/\/www.randform.org\/blog\/?p=1550","title":{"rendered":"Collatz conjecture"},"content":{"rendered":"
collatz353-125.png<\/div>\n

Who says all the unsolved math problems are difficult to phrase?
\nThe Collatz conjecture can be phrased as a simple question: Start with a positive number. If the number is even take its half otherwise take 3 times the number plus 1. Now do this over and over again. The (yet unanswered) question is: will this process allways reach the number 1?
\n(from there the sequence of numbers gets into a boring 1, 4, 2, 1,… cycle)
\nThe conjecture is “yes” and it has been shown to be true for numbers up to 10 * 258<\/sup>, but this is of course no big evidence.
\nThe above image shows the numbers when starting with 353. It takes 125 iterations to reach 1 in this case and the biggest intermediate value is 9232.
\nThere are some nice reformulations of the problem. One can for example state it as a a 2-tag system<\/a>
\nThe 2-tag sequence for 7 follows below
\n
\n
\n1111111
\n11111-+
\n111-+-+
\n1-+-+-+
\n+-+-+-+
\n+-+-+111
\n+-+111111
\n+111111111
\n11111111111
\n111111111-+
\n1111111-+-+
\n11111-+-+-+
\n111-+-+-+-+
\n1-+-+-+-+-+
\n+-+-+-+-+-+
\n+-+-+-+-+111
\n+-+-+-+111111
\n+-+-+111111111
\n+-+111111111111
\n+111111111111111
\n11111111111111111
\n111111111111111-+
\n1111111111111-+-+
\n11111111111-+-+-+
\n111111111-+-+-+-+
\n1111111-+-+-+-+-+
\n11111-+-+-+-+-+-+
\n111-+-+-+-+-+-+-+
\n1-+-+-+-+-+-+-+-+
\n+-+-+-+-+-+-+-+-+
\n+-+-+-+-+-+-+-+111
\n+-+-+-+-+-+-+111111
\n+-+-+-+-+-+111111111
\n+-+-+-+-+111111111111
\n+-+-+-+111111111111111
\n+-+-+111111111111111111
\n+-+111111111111111111111
\n+111111111111111111111111
\n11111111111111111111111111
\n111111111111111111111111-+
\n1111111111111111111111-+-+
\n11111111111111111111-+-+-+
\n111111111111111111-+-+-+-+
\n1111111111111111-+-+-+-+-+
\n11111111111111-+-+-+-+-+-+
\n111111111111-+-+-+-+-+-+-+
\n1111111111-+-+-+-+-+-+-+-+
\n11111111-+-+-+-+-+-+-+-+-+
\n111111-+-+-+-+-+-+-+-+-+-+
\n1111-+-+-+-+-+-+-+-+-+-+-+
\n11-+-+-+-+-+-+-+-+-+-+-+-+
\n-+-+-+-+-+-+-+-+-+-+-+-+-+
\n-+-+-+-+-+-+-+-+-+-+-+-+1
\n-+-+-+-+-+-+-+-+-+-+-+11
\n-+-+-+-+-+-+-+-+-+-+111
\n-+-+-+-+-+-+-+-+-+1111
\n-+-+-+-+-+-+-+-+11111
\n-+-+-+-+-+-+-+111111
\n-+-+-+-+-+-+1111111
\n-+-+-+-+-+11111111
\n-+-+-+-+111111111
\n-+-+-+1111111111
\n-+-+11111111111
\n-+111111111111
\n1111111111111
\n11111111111-+
\n111111111-+-+
\n1111111-+-+-+
\n11111-+-+-+-+
\n111-+-+-+-+-+
\n1-+-+-+-+-+-+
\n+-+-+-+-+-+-+
\n+-+-+-+-+-+111
\n+-+-+-+-+111111
\n+-+-+-+111111111
\n+-+-+111111111111
\n+-+111111111111111
\n+111111111111111111
\n11111111111111111111
\n111111111111111111-+
\n1111111111111111-+-+
\n11111111111111-+-+-+
\n111111111111-+-+-+-+
\n1111111111-+-+-+-+-+
\n11111111-+-+-+-+-+-+
\n111111-+-+-+-+-+-+-+
\n1111-+-+-+-+-+-+-+-+
\n11-+-+-+-+-+-+-+-+-+
\n-+-+-+-+-+-+-+-+-+-+
\n-+-+-+-+-+-+-+-+-+1
\n-+-+-+-+-+-+-+-+11
\n-+-+-+-+-+-+-+111
\n-+-+-+-+-+-+1111
\n-+-+-+-+-+11111
\n-+-+-+-+111111
\n-+-+-+1111111
\n-+-+11111111
\n-+111111111
\n1111111111
\n11111111-+
\n111111-+-+
\n1111-+-+-+
\n11-+-+-+-+
\n-+-+-+-+-+
\n-+-+-+-+1
\n-+-+-+11
\n-+-+111
\n-+1111
\n11111
\n111-+
\n1-+-+
\n+-+-+
\n+-+111
\n+111111
\n11111111
\n111111-+
\n1111-+-+
\n11-+-+-+
\n-+-+-+-+
\n-+-+-+1
\n-+-+11
\n-+111
\n1111
\n11-+
\n-+-+
\n-+1
\n11
\n-+
\n1
\n<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"

Who says all the unsolved math problems are difficult to phrase? The Collatz conjecture can be phrased as a simple question: Start with a positive number. If the number is even take its half otherwise take 3 times the number plus 1. Now do this over and over again. The (yet unanswered) question is: will […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1550"}],"collection":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1550"}],"version-history":[{"count":0,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1550\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}