# [seqfan] Re: Smallest prime wich is equal to a multiple of his reversal +/- a prime smaller than him in n ways

Neil Sloane njasloane at gmail.com
Mon Mar 12 04:47:14 CET 2012

```The message ends with the question
> So the sequence begins 31, 41, ?, 61, 6421, 8501,...
I guess this asks for the smallest prime p for which there are n solutions,
for n=1,2,3,...
But p=71 has three solutions:
71 = 2*17 +37
71 = 4*17 + 3
71 = 6*17 - 31,
so surely the sequence begins 31, 41, 71, 61, 6421, 8501, ... ?
Or am I missing something? The next term, if it exists, is > 48000.
Neil

On Sun, Dec 11, 2011 at 11:15 PM, Alonso Del Arte
<alonso.delarte at gmail.com>wrote:

> I find it interesting, but for the sake of those of us who can't read
> Spanish, it should be noted what the constraint is on a (that a < p),
> because otherwise we can choose any value of a that we like.
>
> Al
>
> On Sun, Dec 11, 2011 at 4:59 PM, Claudio Meller <claudiomeller at gmail.com
> >wrote:
>
> > Hi seqfans:
> >
> > In
> >
> >
> http://simplementenumeros.blogspot.com/2011/12/833-igual-un-multiplo-del-inverso-mas.html
> >  I put this problem :
> >
> > 31 is the smallest prime wich is equal to a multiple of his reversal (13)
> > +/- a
> >
> > prime smaller than him:
> >
> > 31 = 13 x 2 + 5
> >
> > 41 is the first with two solutions
> > 41 = 14 x 2 + 13
> > 41 = 14 x 5  - 29
> > 61 has four solutions :
> >
> > 61 = 16 x 2 + 29
> > 61 = 16 x 3 + 13
> > 61 = 16 x 4  -   3
> > 61 = 16 x 5  - 19
> >
> > with five and six solutions :
> >
> > 6421 = 1246 x 2 + 3929
> > 6421 = 1246 x 3 + 2683
> > 6421 = 1246 x 5 + 191
> > 6421 = 1246 x 8  - 3547
> > 6421 = 1246 x 9  - 4793
> >
> >
> > 8501 = 1058 x 6 + 2153
> > 8501 = 1058 x 8 + 37
> > 8501 = 1058 x 9  - 1021
> > 8501 = 1058 x 11  - 3137
> > 8501 = 1058 x 14  - 6311
> > 8501 = 1058 x 15  - 7369
> >
> > So the sequence begins 31, 41, ?, 61, 6421, 8501,
> > Is this of interest?
> > --
> > Claudio Meller
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>

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