# [seqfan] Re: A1: In binary representation, a(n)^2 is the smallest square with n^2 as substring.

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Tue Aug 18 16:19:04 CEST 2009

```Your sequence reminds me of one kind of sequences I have been submitting lately.
:)

But since binary m is a substring of binary m, you should add to the definition that a(n) > n. As it is written now, a(n) would equal n for all n, if I understand right.

Thanks,
Leroy Quet

[ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]

--- On Tue, 8/18/09, zak seidov <zakseidov at yahoo.com> wrote:

> From: zak seidov <zakseidov at yahoo.com>
> Subject: [seqfan]  A1: In binary representation, a(n)^2  is the smallest square with n^2 as substring.
> To: seqfan at seqfan.eu
> Date: Tuesday, August 18, 2009, 5:09 AM
> While OEIS on vacation...
>
> %N A1 In binary representation,
> a(n)^2  is the smallest square
> with n^2 as substring.
>
> %S 2,3,5,8,10,10,14,16,18,20,22,17,26,28,30,32,34,36,38,
> 40,42,44,46,40,50,52,54,56,58,60,62,64,66,68,70
>
> %C
> In most cases a(n)=a(n-1)+2 but the sequence is not
> monotonic:
>
> the terms a(n) which are less than previous ones,
> a(n)<a(n-1), are:
> a(n)=17,40,80,99,160,320,640,577,1280,
> with corresponding n: 12,24,48,70,96,192,384,408,768.
>
> Q Are all n=12*k giving a(n)=40*k for k>2?
>
> %e
> a(12)=17 because 12^2=144=10010000_2, and
> 17^2=289=1010001(10010000)01_2.
>
> See
> http://zak08.livejournal.com/14344.html
>
> Thanks,
> Zak
>

```