# [seqfan] Re: Middle digit in square numbers

Neil Sloane njasloane at gmail.com
Mon Dec 12 17:29:26 CET 2016

```All those suggestions are definitely worth adding to the OEIS!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Mon, Dec 12, 2016 at 6:01 AM, Olivier Gerard <olivier.gerard at gmail.com>
wrote:

> There is an interesting phenomena going on with
> a related sequence
>
> numbers whose square has an even number of digits
> in base 10 and the two middle digits are equal.
>
> 83^2 = 6889 is in this sequence.
>
> 35, 38, 46, 65, 76, 83, 85, 318, 335, 348, 359, 380, 383, 393, 400,
> 415, 419, 432, 436, 441, 457, 469, 500, 511, 526, 527, 585, 586, 599,
> 600, 611, 620, 636, 648, 654, 665, 688, 692, 696, 700, 711, 718, 728, ...
> (not yet in the OEIS, will be A279410)
>
> For certain modulo (such as 43, 61, 75) the residues display nice
> patterns close to concentric hyperboles (compute it at least up to 5000
> to see them correctly).
>
>
> Olivier
>
>
> On Mon, 12 Dec 2016 at 11:30 Jeremy Gardiner <jeremy.gardiner at btinternet.
> com>
> wrote:
>
> >
> > Consider also cubes:
> >
> > 0: 0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199,
> > 1: 1, 6, 8, 23, 44, 45, 102, 106, 110, 114, 117, 121, 137, 148, 152, 153,
> > 2: 5, 9, 103, 113, 133, 146, 151, 154, 165, 180, 198,
> > 3: 29, 34, 39, 46, 118, 125, 141, 142, 155, 161, 170,
> > 4: 7, 104, 112, 140, 143, 158, 166, 186, 188, 195,
> > 5: 26, 43, 107, 109, 119, 122, 136, 139, 144, 150, 177, 179, 197,
> > 6: 22, 25, 27, 36, 37, 124, 129, 134, 147, 156, 160, 169,
> > 7: 31, 32, 105, 111, 128, 130, 149, 167, 173, 191, 192,
> > 8: 2, 24, 35, 38, 120, 127, 131, 138, 145, 172, 174, 182, 183,
> > 9: 28, 33, 41, 108, 132, 157, 159, 175, 178, 181, 184, 187, 190, 193,
> 196,
> >
> >
>
> --
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>

```