[seqfan] Re: A115159 looks incorrect

David Wilson davidwwilson at comcast.net
Wed Aug 17 14:29:48 CEST 2011

I don't think it's a boundary condition issue. I rechecked, and all of
the listed elements
are in fact sums of positive triangle + square + cube. The numbers that
are not are in
A115162. I think the title is incorrect, but I can't guess what it
should be.

Anyway, does every nonnegative integer = nonnegative triangle + square +
cube?

34 = 10+16+8
63 = 6+49+8
89 = 45+36+8
99 = 66+25+8
139 = 10+121+8

On 8/17/2011 1:10 AM, Alonso Del Arte wrote:
> What if instead of nonnegative we say "positive" across the board, to rule
> out 0^2 and perhaps rescue 63 and 99?
>
> However, Giovanni's remark "There are 718 such numbers up to 2*10^9" makes
> me think there is some other requirement he neglected to communicate.
>
> Al
>
> On Tue, Aug 16, 2011 at 11:22 PM, David Wilson<davidwwilson at comcast.net>wrote:
>
>> A115159 purports to be numbers which are not the sum of a nonnegative
>> triangle, square and cube.
>>
>> However, every listed element is indeed such a sum, starting with:
>>
>> 34 = 10+16+8
>> 63 = 55+0+8
>> 89 = 45+36+8
>> 99 = 91+0+8
>> 139 = 10+121+8
>> ...
>>
>> and I could supply the rest on request.  In fact, I could find no
>> nonnegative integers<= 50000 that are in
>> the sequence, and I would venture that every nonnegative integer is a such
>> a sum.
>>
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