[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.
Phone: 732 828 6098; home page: http://NeilSloane.com
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
>
>
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