S_{0,4}

[Max]

On 2/20/06, koh <zbi74583 at boat.zero.ad.jp> wrote:
>     Hi, Max.
>     S_{0.4} :
>     Thank you for verifying my calculation.
>     And I am sorry that I did a typo mistake.
>     The correct number is 5500000011111.
>     Many "Open end" {0,4}-Aliquot sequences seem to exist.

Starting with 5500000011111 I was able to complete 3680 iterations
until I came up to the need of factorization of 345-bit number:

53745739035525498795880532110461237696331778423865306564243673498785024002833035483307382497112648461303

I'm going to factor it with NFS later and continue.

If you have any other interesting starting values, I can try them out.

Max

> > On 2/16/06, koh <zbi74583 at boat.zero.ad.jp> wrote:
> >>     [Definition of {k.l}-Aliquot sequence]
> >>     Let S(n)=Sigma(n)/l-k*n
> >>     a_{m}=S(a_{m-1})
> >>
> >>
> >>
> >>     I also tried to  find a {0,4}-Aliquot sequence which goes to
> >> infinity.
> >>     I input  a_1= 555500000011111, and  it became a number of 184 digits
> >> after 850 steps .
> >>    It seems to go to infinity.
> >>    But I am not sure.
> >
> > After 10 steps I've got non-integer number. Please take a look:
> >
> > ? ss(n) = sigma(n)/4
> >
> > ? a=555500000011111; for(i=1,10,a=ss(a);print1(", ",a))
> > , 138875019381828, 95002193790000, 100966126897152, 89923161968640,
> > 109622213986656, 88824291655680, 100121345533440, 121380998618880,
> > 171368541388800, 395052880195809/2
> >
> > Max
> >
>
>