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

Charles Greathouse charles.greathouse at case.edu
Fri Nov 11 15:57:20 CET 2011

```No, scratch that.  I can show that the sequence is well-defined
through ten million.  No general proof yet, though.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

2011/11/11 Charles Greathouse <charles.greathouse at case.edu>:
> The next non-obvious number is 92.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> 2011/11/11 Charles Greathouse <charles.greathouse at case.edu>:
>> 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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>>
>

```