Yesterday Sally cleverly observed that 2015 is a palindrome in binary. Which got me wondering whether there could be any years that are palindromes in both binary and decimal.<\/p>\n
So I wrote a little javascript program to search for them. After several hours of crunching, my computer found 36 such years, from the year one through the year 75015151057, which in binary is:<\/p>\n
<\/p>\n
<\/p>\n
The most recent year on the list was 717 AD, and the next one won’t be until 7447 AD, so don’t hold your breath.<\/p>\n
Are there infinitely many such years, or is there a largest one? Somebody would need to come up with a mathematical proof, but I can make a guess just from looking at the numbers.<\/p>\n
As I look down the list, the number of digits is increasing at a pretty constant rate. That’s what mathematicians call a logarithmic distribution. If that pattern continues, then the sequence will go on forever.<\/p>\n
If that’s true, then no matter how far out in the future you go, there will always be another year that is a palindrome in both base two and base ten. Although you probably won’t be able to get to most of them without a Tardis.<\/p>\n","protected":false},"excerpt":{"rendered":"
Yesterday Sally cleverly observed that 2015 is a palindrome in binary. Which got me wondering whether there could be any years that are palindromes in both binary and decimal. So I wrote a little javascript program to search for them. After several hours of crunching, my computer found 36 such years, from the year one … Continue reading “In the year 75015151057”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/15595"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=15595"}],"version-history":[{"count":7,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/15595\/revisions"}],"predecessor-version":[{"id":15602,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/15595\/revisions\/15602"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15595"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}