seq A100661

[Joerg Arndt]

* Ralf Stephan <ralf at ark.in-berlin.de> [Jun 11. 2006 12:03]:
> You wrote 
> > http://www.research.att.com/~njas/sequences/A100661
> > 
> > The following _seems_ to be true:
> > 
> > OGF =  \frac{2\,(1-x)\,\prod_{n=1}^{\infty}{\left(1+x^{2^n-1}\right)} - 1}{(1-x)^2}
> 
> Intuitively, this is all true as, from experience, if you start with
> such OGFs (sums or products where x is to the 2 to the index) you
> will get sequences that have connecions to the binary representation.

Intiutively clear for me, too.
Just wanted to check whether I can add the commnest as truths.
Now I marked them conjecture.
(except for the greedy computation, which can
 be shown to give the correct result)

> The OEIS is full of such sequences.

And I find them very often useful.


> 
> 
> ralf