[seqfan] Re: Sums of two sequences

Jonathan Post jvospost3 at gmail.com
Sun Mar 7 01:52:50 CET 2010

```There would be fewer than A000217(169) = 14365 core+core sumsets to
check. That's because some give trivial sumsets, such as with A000012
the all 1's sequence.

It is therefore feasible to automatically generate the fewer than
14000 nontrvial core+core sumsets, and see if any of these are
(possibly with offset or constant factor) some other core sequence.

Further, some can easily be solved analytically, as with many sums of
different kinds of figurate numbers.

My hunch is that there would be at least one publishable hit, and
several fun conjectures.

Feel free to footnote me and Zak in the paper, when someone does so!

Best,

Jonathan Vos Post

On Sat, Mar 6, 2010 at 2:59 PM, zak seidov <zakseidov at yahoo.com> wrote:
> But is it possible (and worthwhile) to include in superseeker such additional option only for CORE sequences
> (just 169(?!) at present)?
>
> The same is for other transformations.
>
> Just a thought,
> Zak
>
> --- On Sat, 3/6/10, N. J. A. Sloane <njas at research.att.com> wrote:
>
>> From: N. J. A. Sloane <njas at research.att.com>
>> Subject: [seqfan] Re: Sums of two sequences
>> To: seqfan at list.seqfan.eu
>> Cc: njas at research.att.com
>> Date: Saturday, March 6, 2010, 4:42 PM
>> > has someone automatically tested
>> this property - is a(n) in OIES forall
>> S(n), T(n) in OIES?
>> seems doable...
>>
>> superseeker doesn't seem to recognize this case.
>>
>>
>> Me:  it's at least quadratic in the size of the OEIS.
>> If one were doing it systematically one would have
>> to try several different choices for the difference
>> in offset between the 2 sequences.
>>
>> In fact it would be nice to check a query sequence
>> against all small integer combinations
>>
>>       alpha S(n) + beta T(n+epsilon)
>>
>> where S, T are in the OEIS.   Superseeker
>> doesn't do
>> it because it is quadratic, and Superseeker runs
>> on my local machine.  But it would certainly be a nice
>>
>> thing to include in Superseeker.
>> I'm open to suggestions of ways it might be implemented.
>>
>> Neil
>>
>>
>>
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