tag:blogger.com,1999:blog-6757805.post9067746141912956669..comments2018-05-05T22:45:41.037ZComments on Ken's blog: [tdoyjpic] Testing the Collatz conjecture on 10-million-bit numbersKennoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6757805.post-54758778438793068792017-09-22T10:00:37.794Z2017-09-22T10:00:37.794ZThe Collatz Conjecture - "Calm Zones" - ...The Collatz Conjecture - "Calm Zones" - Can you help?<br /><br />Defining the function col(n) as that which returns the length of the sequence "draining" n (the seed) to 1, then we know that there is no connection between col(n) to col (n+1).<br /><br />However, there are "Calm Zones" of length L where col(n) = col(n+1) = col(n+2) = ... = col(n+L-2) = col(n+L-1) for some n.<br />Example: a Calm Zone of length 716 starts at n=164,557,897,218.<br /><br />My (intuitively plausible) supposition is that for any finite positive integer L there exists a value n where a Calm Zone of length L starts.<br /><br />I have also scanned all seeds up to 266,256,000,000 and didn't find any larger Calm Zone.<br /><br />Where are larger Calm Zones? my computer is too slow...Ronnie Ginzburghttps://www.blogger.com/profile/07956185969831062824noreply@blogger.com