Doubly recursive sequence

[Edwin Clark]

On Sun, 3 Aug 2003, Christian G. Bower wrote:

> 
> 
> Leroy Quet <qqquet at mindspring.com> wrote:
> ...
> > Interesting. 
> > 
> > I am slightly curious about such things such as: 
> > for which indexes k, does a[k] = 1,
> > or when is a[k] < a[k-1] ?
> > 
> > And what would be the sequence of differences between consecutive k's, 
> > where
> > a[k] < a[k-1]?
> > 
> > 
> > (The k's where a[k] = 1 are 0, 1, 4, and 64, for k < 100 {as seen from 
> > the list generated by Farideh Firoozbakht}. These k's, except the 0, all 
> > happen to be powers of 2; but this is much too small a sample to deduce 
> > anything, obviously.)
> 
> I get 400 and 489 as the next 1's of a[k]. Although my calculations can
> overflow. I don't believe they did in this case, but I'd have to spend
> a little time verifying it to make sure.
> 
> 
> 
> 

I get the following values of n <= 10^4 where a[n] = 1:

  
             0, 1, 4, 64, 400, 489, 519, 2164, 3589, 8703

(using Maple.)

---Edwin