A "doublely-recursive" sequence

[f.firoozbakht at sci.ui.ac.ir]

 Hello,Leroy Quet,

 Christian G. Bower wrote:

>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.

 The k's where a[k]= 1 are 0,1,4,64,400,489,519,2164,3589 and 8703 for
 k < 48000.!!


Regards,

Farideh Firoozbakht
UniverSity of Isfahan,Iran 
f.firoozbakht at sci.ui.ac.ir





>Quoting Leroy Quet <qqquet at mindspring.com>:

> 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.)
> 
> Hmmm...I also wonder what the plot of this sequence, perhaps scaled 
> logarithmically, looks like.
> 

 


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