[seqfan] Binary digits change sequences
Ali Sada
pemd70 at yahoo.com
Tue Aug 13 15:27:54 CEST 2019
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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