A Generalization of the Sequence Convergence Problem

[Hans Havermann]

> >I believe a(n)-->1/2, which can lead to conjectures related to primes.
>  
> This is possible, but is not suggested by the graph of (n, a(n)) from 
> n = 1 to 10^5. (Of course, the convergence to 1/2 could be clear from 
> looking at larger n, so the graphical evidence isn't the last word 
> either.)

For what it's worth, I've put up a picture of the graph:

http://odo.ca/~haha/j/num/osc.jpg

If you refresh the URL in about 24 hours, I should have it extending to 
10^6.