wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
riddles >> hard >> More hailstone numbers
(Message started by: JocK on Jun 25th, 2005, 8:42am)

Title: More hailstone numbers
Post by JocK on Jun 25th, 2005, 8:42am
Starting from a positive integer k, one can generate a series of integers by iterating the mapping:

k' = k/2   if k even,

k' = (3k+5n)/2 if k odd.

Here, n is an odd positive integer constant.

Can you find a starting value and a n-value for which the iteration fails to yield a value not exceeding 347n?





Title: Re: More hailstone numbers
Post by Barukh on Jun 26th, 2005, 11:43pm
[hideb]
The minimal solution I've found is: n = 29, k = 12655. It generates a 66-long cycle with minimal element 19055.

Of course, this was achieved using computing power. Currently, I have no idea how to tackle this problem more intelligently.
[/hideb]



Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board