A "doublely-recursive" sequence

[Edwin Clark]

Hi Farideh,

I guess our numbers must be correct then. I'd bet that the sequence
is infinite but grows very slowly. If you find anymore numbers you should
add them to the sequence I submitted yesterday to the EIS. 

There is nothing special about 1. One could just as well find the indices
where the original sequence was 2 or 4 or any number in the sequence.  

I seem to have lost my original data up to 10^5. But I redid it up to 10^4
and found that the most frequently occuring number in Leroy's original
sequence up to 10^4 is 2996 which occurs 37 times. :-)

Cheers,

Edwin

On Mon, 4 Aug 2003 f.firoozbakht at sci.ui.ac.ir wrote:

> 
> Hello, Edwin,
> 
> I have found the numbers 0,1,4,64,400,489,519,2164,3589,8708 and 84761
> just like you,but I haven't stopped the process yet.
> 
> Farideh
> 
> 
> 
> 
> 
> Quoting Edwin Clark <eclark at math.usf.edu>:
> 
> > On Sun, 3 Aug 2003 f.firoozbakht at sci.ui.ac.ir wrote:
> > 
> > > 
> > > 
> > >  The k's where a[k]= 1 are 0,1,4,64,400,489,519,2164,3589 and 8703
> > for
> > >  k < 48000.!!
> > > 
> > > 
> > 
> > 
> > Just finished checking out to 10^5. Here are the values of k such that
> > a[k] = 1 in this range:
> > 
> >    0, 1, 4, 64, 400, 489, 519, 2164, 3589, 8703, 84761
> > 
> > It is interesting that the last number 84761 is prime. At Neil's
> > suggestion I will add this to the EIS.
> > 
> > Edwin
> > 
> > 
> > 
>