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

[Charles Greathouse]

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.
>>
>> Franklin T. Adams-Watters
>>
>> -----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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