|SUMit Roster Software > Nut's Weekly > February 2002 > Crossroad||Nederlands · Search...|
|Monday, 25 February 2002||December 2001 January 2001 Bean Expired Immigrant March 2001 April 2002|
Do all paths end at 1?The diagram above shows that all paths for numbers up to 17 end in 1. Yet, I haven't seen a convincing proof yet for all numbers.
However, the conjecture has not been proven wrong either. All numbers checked so far have a path leading to 1 (computrain.nl/...).
MultipowersIt's easy to check the multi powers of two (4, 8, 16, 32, 64, 128, ...). They are at the bottom of the diagram, at the highway towards 1. The path for all odd numbers ends on this highway with 16 -> 8 -> 4 -> 2 -> 1.
The number of steps leading to one seems a bit unpredictable, but roughly speaking it is a logaritmic function
That should not be a big surprise.
Lots of other paths run parallel to
CrossroadsAn endless number of paths can only end up in one point through sufficient
bifurcations, looking bottom to top. 5 divides at 10 into 3 and 20.
There are many bifurcations, 1/6 of all numbers (6n+4): 4, 10, 16, ...
Ulam's conjecture will be proven,Till next week,