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

Georgi Guninski guninski at guninski.com
Fri Nov 11 15:33:45 CET 2011

```I suppose the abc conjecture puts bound on x in terms of n if gcd(6,n) =
1.
Small n and big x will give abc triples of high quality and these are
quite rare.

abc may bound even without the gcd condition.

On Fri, Nov 11, 2011 at 09:24:01AM -0500, Charles Greathouse wrote:
> 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(issquare(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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```