A007666

[Jon Schoenfield]

SeqFans,

In looking recently at some of the sequences with keywords "hard" and 
"nice," my first impression regarding A007666 was that it didn't seem as 
though it should be so hard to check for all possible values of a(6) up 
through 1000 or so.  However, after my program, which had started off 
nicely, slowed to a crawl while still checking values far short of 1000, I 
changed my opinion....   :-/

Since the entry in the "Extensions" field says, "The next term has been 
claimed to be 1141, but this is incorrect," I decided to verify this, and my 
program is slowly crunching away, now looking only for a set of six 6th 
powers whose sum is exactly 1141^6.  Thus far, the closest set it has found 
is 211^6 + 432^6 + 454^6 + 776^6 + 836^6 + 1085^6 = 1141^6 - 23.

I imagine there are much faster ways of doing this than the approach I'm 
using.  Has anyone on the SeqFan list verified that A007666(6) isn't 1141? 
Has anyone tested whether perhaps A007666(6) = 1411, in case the claim 
regarding 1141 was the result of a transposition error?  Also, does anyone 
have an opinion as to whether it'd be worthwhile for the OEIS entry for 
A007666 to say something like "a(6), if a solution exists, is at least" ... 
and give a known lower bound?

Thanks,

-- Jon