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

[franktaw at netscape.net]

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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>
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>

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