# [seqfan] Re: Squares with even-positioned digits matching the original number

israel at math.ubc.ca israel at math.ubc.ca
Sun Dec 3 05:33:12 CET 2023

```This is analogous ro 2164`8, not David's sequence, because David is
removing the units digit, 10^2's digit etc., and you're keeping those
digits and removing the others.

Cheers,
Robert

On Dec 2 2023, W. Edwin Clark wrote:

>The analogous sequence for base 2 has lots of small values easily computed:
>
>
> 1,2,4,5,8,10,16,17,20,21,32,34,40,42,64,65,68,69,80,81,84,128,130,136,138,160,162,168,256,257,260,261,272,273,276,277,320,321,324,336,337,512,514,520,522,544,546,552,554,640,642,648,672,674,1024,1025,1028,1029,1040,1041,1044,1045,1088,1089,1092,1093,1104,1108,1280,
>
>For example, let r(n) be the base 2 representation of n then
>r(20) = [1, 0, 1, 0, 0]
>r(400 )= [1, 1, 0, 0, 1, 0, 0, 0, 0]
>
> On Fri, Dec 1, 2023 at 2:54PM David Radcliffe <dradcliffe at gmail.com>
> wrote:
>
>> Hi all,
>>
>> I recently came across sequence A326418, which is described as
>> "Nonnegative numbers k such that, in decimal representation, the
>> subsequence of digits of k^2 occupying an odd position is equal to the
>> digits of k." I was wondering about the analogous problem for even
>> positions, but that sequence is not in the OEIS.
>>
>> I performed a search up to 10^16, and the only example I found was k =
>> 9678692507732, excluding multiples of 10.
>>
>> This is a term because k^2 = 93677088659227550879783824, and if we remove
>> every other digit from k^2, starting with the units digit, we get back to
>> 9678692507732.
>>
>> Are there other solutions? I am intrigued by this sequence because the
>> first term is so large, but I don't know enough terms to propose it for
>> inclusion in the OEIS.
>>
>> - David
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
```