tag:blogger.com,1999:blog-3722233.post6364597152143042105..comments2024-11-03T21:27:06.200-06:00Comments on Computational Complexity: An interesting serendipitous numberLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3722233.post-20642217771333867372020-09-20T06:38:27.752-05:002020-09-20T06:38:27.752-05:00Suddenly invented the following
scientific papersâ€™...Suddenly invented the following<br />scientific papersâ€™ references paradox:<br /><br />https://www.youtube.com/watch?v=CMFcmutIEy4<br /><br />Yuly Shipilevskyhttps://www.blogger.com/profile/13699450530150796472noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90146168831337914532020-09-19T14:00:34.217-05:002020-09-19T14:00:34.217-05:00This reminded me of how, as n -> Inf, (1 + 1/n)...This reminded me of how, as n -> Inf, (1 + 1/n)^n is about e. So I could imagine that, for "large enough" n, if x_n is "a bit more than" n, then 1/x_n is "a bit less than" 1/n, and x_{n+1} is "somewhat less than" e. Which means that x_{n+2} will have something^{n+2}, which seemed apt to be even larger. So it seemed like it should oscillate, at least sometimes. (Also, induction shows that x_n >= 1 always.)<br /><br />At that point, I basically punted: by writing the five lines of Python to see that this happened (at least sometimes), and looking at the solution in this post :/<br />Josh Burdickhttps://www.blogger.com/profile/12231348292069164630noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24669255451795095992020-09-14T11:50:14.380-05:002020-09-14T11:50:14.380-05:00The article is easily found... For instance https:...The article is easily found... For instance https://doi.org/10.1007/978-1-4471-0751-4_8 . Of course, it is behind a paywall, but then Sci-hub comes to rescue and you find the complete book: http://libgen.rs/book/index.php?md5=231BF372E8C89E575F5A4A0C89D687A6B.noreply@blogger.com