
Re: Max. power of 2 and number of odd integers in a loop in the Collatz problem
Posted:
Jun 4, 2009 8:06 AM


On Jun 3, 10:41 pm, Mensanator <mensana...@aol.com> wrote: > On Jun 3, 4:43 am, roupam <roupam.gh...@gmail.com> wrote: > > > I have found, that if there exists a loop, then if > > n = number of odd integers in the loop > > k = maximum power of 2 that divides a number in the loop > > then, the following conclusions hold... > > for positive integers > > k <= n+1 > > for negative integers > > k < n log3//log2  n + 1 > > Consider the negative loop starting with > > 17 50 25 74 37 110 55 164 82 41 122 61 182 91 272 136 > > 68 34 and then back to 17 > > Here... > > n = 7 > > k = 4 > > 4 < 7 * log3/log2 7 + 1 = 5.09... > > What does this follow from, other than your observation? >
I have a proof for it...

