# [seqfan] Re: Binary digits change sequences

Neil Sloane njasloane at gmail.com
Tue Aug 13 22:45:51 CEST 2019

```Ali,  Yes, they are worth adding to the OEIS, all of them (well, not too
many!).
Sequences like this have applications in many areas including cryptography.

The classic reference is Joerg's book:

Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational
(The Fxtbook)</a>

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 Tue, Aug 13, 2019 at 2:24 PM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

> Hi Everyone,
>
>
> Please see the sequences below. I just want to check if theywere
> “legitimate” to be added to OEIS.
>
> The definition “Number of digits that change when we multiplynatural
> numbers by 2 in the binary system” gives us:
>
>
> 2,2,2,2,4,2,2,2,4,4,4,2,4,2,2,2,4,4,4,4,6,4,4,2,4,4,4,2,4,2,2,2,4,4,4,4,6,4,4,4,6,6,6,4,6,4,4,2,4,4,4,4,6,4,4,2,4,4,4,2,4,2,2,2,4,4,4,4,6,4,4,4,6,6,6,4,6,4,4,4,6,6,6,6…….
>
>  (For example.101*10=1010. All 4 digits changed, so a(5)=4.)
>
> I couldn’t find this sequence. However, when I divided eachterm by 2, I
> got A069010 (except for the zero at the start.)
>
>
>
> Also, with the same definition but multiplying by 3instead of 2, I got
>
>
> 1,1,2,1,2,2,2,1,2,2,3,2,3,2,2,1,2,2,3,2,3,3,3,2,3,3,3,2,3,2,2,1,2,2,3,2,3,3,3,2,3,3,4,3,4,3,3,2,3,3,4,3,4,3,3,2,3,3,3,2,3,2,2,1,2,2,3,2,3,3,3,2,3,3,4,3,4,3,3……
>
> Which is A007302, except for the initial zero again.
>
>
>
> When I repeated the definition, multiplying by 4 this time, Igot
>
>
> 2,2,4,2,2,4,4,2,4,2,4,4,4,4,4,2,4,4,6,2,2,4,4,4,6,4,6,4,4,4,4,2,4,4,6,4,4,6,6,2,4,2,4,4,4,4,4,4,6,6,8,4,4,6,6,4,6,4,6,4,4,4,4,2,4,4,6,4,4,6,6,4,6,4,6,6,6,6,6,2….
>
> Maybe I didn’t look well, but I couldn’t find this one evenwhen I divided
> by 2.
> (Is multiplying by even numbers always gives us even numbers of digit
> changes? And if so,why?)
>
> I am working on multiplying by more numbers. I am alsoworking on
> base-3,4,5,… systems.
>
> I would appreciate any feedback.
>
>
>
> Best,
>
>
>
> Ali
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```