[seqfan] Re: Numbers that are the sum of x nonzero y-th powers

[Marc LeBrun]

To actually fix it, someone could either
   1. change the title to "numbers that are a sum of 7 numbers in 1 through 5 raised to the 8th power"
or 2. change the sequence values so they actually include all the numbers

(I recommend #2, although it's more work).

At the very least, some comment should be quickly added to warn users that the sequence as it stands is incorrect.


> On Jul 31, 2020, at 4:11 PM, David Corneth <davidacorneth at gmail.com> wrote:
> 
> Hi All,
> 
> I just came across A003385 which is called:
> Numbers that are the sum of 7 nonzero 8th powers.
> 
> And there is a whole series of such sequences, starting at about A003325
> going through A003400.
> 
> I think at least some but still quite many need the following fixes.
> The most important ones are b-files and progs.
> A003385 has a b-file of 3432 terms, the largest of them being: 117440512.
> However, up to that bound, 3319 terms are missing.
> Possibly it's due to the prog at hand, or at least the idea.
> The prog there is in Mathematica:
> Total/@Tuples[Range[5]^8, 7]//Union
> And such progs are all arround those sequences.
> Now I don't know Mathematica quite well but I looked in the documentation
> and range[5] gives the array [1, 2, 3, 4, 5] and each of these numbers is
> going to be raised to the 8th power, giving:
> [1, 128, 2187, 16384, 78125]. Then some tuples (5^7 of them) are made and
> that makes a list of distinct terms. i.e. duplicates are removed, and there
> will be a lot of duplicates; all permutations of a sorted array of 7
> numbers each in 1 through 5 raised to the 8th power.
> 
> The first missing term in the b-file is 43046727 which is 1^8 + 1^8  + 1^8
> + 1^8  + 1^8  + 1^8  + 9^8.
> Now a quick look shows me a lot of these sequences have such progs.
> Another one is A003384 which has the Mathematica program:
> Union[Total[#^8]&/@Tuples[Range[10], 6]]
> same issue.
> Some look better, like With[{upto=10000},
> Select[Union[Total/@Tuples[Range[Floor[Surd[upto-4, 6]]]^6, 5]], #<=upto&]]
> as in correct but perhaps inefficient.
> in A003361:  Numbers that are the sum of 5 nonzero 6th powers.
> At any rate, I think they need to be revised.
> 
> Some lack a b-file and could have that.
> In some sequences, data could be extended to the 260 chars.
> And probably they could xref each other more.
> And an example or two would be nice.
> 
> What's a good approach here? What changes should actually be made? Who can
> help?
> 
> Best,
> David
> 
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