[seqfan] Re: Fwd: Your A051217 Nonnegative numbers of the form 6^x-y^2.

Charles Greathouse charles.greathouse at case.edu
Fri Nov 11 15:47:28 CET 2011

```Oh yes, I suppose I should look at other moduli.

Of course that just kicks the question higher up: can we always find a
suitable modulus?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Nov 11, 2011 at 9:45 AM,  <franktaw at netscape.net> wrote:
> 6^n - 23 == 3 (mod 5), which is not a square.
>
>
> -----Original Message-----
> From: Charles Greathouse <charles.greathouse at case.edu>
>
> Interesting.  I can prove that the sequence is correct and
> well-defined through 22 (precisely 0, 1, 2, 5, 6, 11, 20 can be
> represented in that form).  But I can't prove that 23 is not a member
> (nor that it is).
>
> I'm just using the standard modular arguments; perhaps there are
> stronger methods to be used here?
>
> I used this very simple GP script:
> is(n)=my(k);if(n==0||n==1,return(1));while(issquare(Mod(-n,6^k++)),if(iss
> quare(6^k-n),return(1)));0
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Thu, Nov 10, 2011 at 10:14 PM, Moshe  Levin <moshe.levin at mail.ru> wrote:
>>
>> Dear Seqfans,
>>
>> Is A051217 (and similars) "well-defined"?
>>
>> Thanks,
>> ML
>>
>>
>> -------- Пересылаемое сообщение --------
>> От кого: Moshe Levin <moshe.levin at mail.ru>
>> Кому: davidwwilson at comcast.net
>> Дата: 10 ноября 2011, 11:30
>> Тема: Your A051217 Nonnegative numbers of the form 6^x-y^2.
>>
>>
>> Dear David,
>> Is  A051217 (and similars) well-defined?
>> Are we sure that, e.g., some integer in ]812, 855[ is not expressible
>
> as
> 6^x-y^2?
>>
>> Thanks,
>> ML
>>
>> %%%%%%%%%%%%%%%%%%%%%%%%%%
>> A051217 Nonnegative numbers of the form 6^x-y^2.
>> {0, 1, 2, 5, 6, 11, 20, 27, 32, 35, 36, 47, 71, 72, 95, 116, 135,
>
> 140, 152,
> 167, 180, 191, 200, 207, 212, 215, 216, 272, 335, 380, 396, 431, 455, 512,
> 551,
> 567, 620, 671, 720, 767, 812, 855, 860, 887, 896, 935, 972, 1007, 1040,
> 1052,
> 1071, 1100, 1127, 1152}
>>
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>>
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```