# [seqfan] Re: Middle digit in square numbers

Andrew Weimholt andrew.weimholt at gmail.com
Mon Dec 12 22:13:27 CET 2016

```Numbers k, such that the middle binary digit of k^2 is 0

0, 2, 4, 5, 8, 9, 10, 16, 17, 18, 19, 22, 32, 33, 34, 35,
36, 37, 40, 41, 44, 64, 65, 66, 67, 68, 69, 70, 71, 76, 77, 80,
81, 84, 85, 87, 90, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138,

Numbers k, such that the middle binary digit of k^2 is 1

1, 11, 20, 21, 38, 39, 42, 43, 45, 72, 73, 74, 75, 78, 79, 82,
83, 86, 88, 89, 140, 141, 142, 143, 148, 149, 150, 154, 155, 158, 159, 162,
163, 166, 167, 169, 170, 172, 173, 175, 178, 180, 181, 272, 273, 274, 275,
276,

Andrew

On Mon, Dec 12, 2016 at 10:28 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> Lars, on the contribution page
> https://oeis.org/Submit.html
> https://oeis.org/edit/allocate
> to allocate some A-numbers, which in my experience are always sequential.
>
> Charles Greathouse
> Case Western Reserve University
>
> On Mon, Dec 12, 2016 at 5:18 AM, Lars Blomberg <larsl.blomberg at comhem.se>
> wrote:
>
> > OK.
> >
> > So 10 A-numbers will be needed.
> > It would facilitate greatly if a sequence like Axxxxx0 .. Axxxxx9 could
> be
> > allocated for this.
> > Is that possible, if so, how?
> > Regards,
> > Lars Blomberg
> >
> > -----Ursprungligt meddelande-----
> > Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För
> israel at math.ubc.ca
> > Skickat: den 12 december 2016 08:39
> > Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Ämne: [seqfan] Re: Middle digit in square numbers
> >
> > Not at all too simple.  Please do contribute them.
> >
> > Cheers,
> > Robert
> >
> > On Dec 11 2016, Lars Blomberg wrote:
> >
> > >
> > >
> > >Hello,
> > >
> > >
> > >
> > >Numbers k such that the middle digit of k^2 is d.
> > >
> > >Obviously k^2 must have an odd number of digits.
> > >
> > >
> > >
> > >Examples for d=4: 2^2 = 4, 12^2 = 144, 21^2 = 441, 29^2 = 841, 102 =
> > >10404, ...
> > >
> > >
> > >
> > >Start of sequences for d =  0..9
> > >
> > >0: 10, 20, 30, 100, 105, 138, 145, .
> > >
> > >1: 1, 110, 119, 123, 127, 131, 142, .
> > >
> > >2: 11, 15, 18, 23, 25, 27, 101, 106,.
> > >
> > >3: 111, 124, 128, 139, 146, 156, 177, .
> > >
> > >4: 2, 12, 21, 29, 102, 107, 116, 120,.
> > >
> > >5: 16, 112, 150, 163, 166, 169, 172,.
> > >
> > >6: 13, 19, 31, 103, 108, 117, 121, .
> > >
> > >7: 24, 26, 113, 137, 144, 154, 181,.
> > >
> > >8: 17, 22, 28, 104, 109, 122, 126, .
> > >
> > >9: 3, 14, 114, 118, 130, 134, 148, .
> > >
> > >
> > >
> > >It was a surprise to me that none of these sequences are in OEIS.
> > >
> > >Maybe they are too simple to be included?
> > >
> > >
> > >
> > >/Lars Blomberg
> > >
> > >
> > >
> > >
> > >--
> > >Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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>

```