A007666

[Jon Schoenfield]

Max,

<<  it is said that only the following ranges (displayed in italic there) 
are finished  >>

Good point!  I hadn't noticed that ... I had just passed on what I'd been 
told.

On the other hand, it says at the home page (http://euler.free.fr/) that the 
Resta page (http://euler.free.fr/resta.htm) was last updated 11/03/2000.  I 
don't know if there's a good source for more current info on any search 
progress ....

In the meantime, perhaps the OEIS entry should have a link to the above 
pages, and the item under "Extensions" should be changed from

    a(6) is either 0 (no solution) or greater than 700000.

to something like

    a(6) is either 0 (no solution) or greater than 272580 (see above link to 
"Resta" page).

-- Jon

----- Original Message ----- 
From: "Max Alekseyev" <maxale at gmail.com>
To: "Jon Schoenfield" <jonscho at hiwaay.net>
Cc: "Robert Gerbicz" <robert.gerbicz at gmail.com>; "Sequence Fans" 
<seqfan at ext.jussieu.fr>; <njas at research.att.com>
Sent: Monday, June 25, 2007 9:46 PM
Subject: Re: A007666


> At http://euler.free.fr/resta.htm it is said that only the following
> ranges (displayed in italic there) are finished:
>
> 0 .. 200000
> 200000 .. 272580
> 300000 .. 350000
> 350000 .. 375012
> 400000 .. 404147
> 450000 .. 468864
> 500000 .. 502464
>
> Is that really true that "they've checked all numbers up to 700,000" ?
> If so, where I can find details?
>
> Max
>
> On 6/10/07, Jon Schoenfield <jonscho at hiwaay.net> wrote:
>>
>>
>> Thanks!
>>
>> So would a comment at A007666 that "a(6) has no solution less than 
>> 700000"
>> be appropriate?
>>
>> Or maybe "a(6) is either 0 (no solution) or greater than 700000"?  Or 
>> would
>> some other wording be better?
>>
>> Thanks again,
>>
>> -- Jon
>>
>> ----- Original Message -----
>> From: Robert Gerbicz
>> To: Sequence Fans
>> Sent: Sunday, June 10, 2007 3:00 AM
>> Subject: [Norton AntiSpam]
>>
>> See http://euler.free.fr/
>> As you can see on their Resta page they've checked all numbers up to
>> 700,000. ( using many modular tricks to speed up the search.)
>> This is a really hard problem, both in running time and memory. But there
>> are known solutions for n=7 and n=8, I don't know if these are the 
>> smallest
>> or not:
>> 568^7=525^7+439^7+430^7+413^7+266^7+258^7+127^7  found by
>> Mark Dodrill in 03/20/1999
>>
>> 1409^8=1324^8+1190^8+1088^8+748^8+524^8+478^8+223^8+90^8
>> found by Scott I. Chase about in 2000.
>
>