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

Olivier Gerard olivier.gerard at gmail.com
Mon Dec 12 00:36:56 CET 2011

```Mr Meller,

If I understand well the constraints you define,
you missed 71 ,401 and 521 among others which have all 3 solutions in base
10.

Example:

71 = 4*17+3 = 2*17+37 = 6*17-31

Regards,

Olivier

On Sun, Dec 11, 2011 at 22:59, 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
>
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>

```