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Timeline for Binary weight of shifted integers

Current License: CC BY-SA 3.0

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Dec 13, 2017 at 22:51 comment added fedja @ShahroozJanbaz OK, I'll think of it a bit more. No promises though ;-)
Dec 13, 2017 at 10:52 comment added Shahrooz Thanks dear @fedja, your proof is nice. For the reverse one, I have no a general idea. Some cases can be checked by coding theory techniques if I have a closed formula for the number of ones in the vector $X_2(n)$, which we know there is not any hope. For example (for coding techniques) you can see page $275$ (and some other pages) of the book "Fundamentals of Error Correcting Codes".
Dec 12, 2017 at 5:09 history edited fedja CC BY-SA 3.0
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Dec 12, 2017 at 5:03 history edited fedja CC BY-SA 3.0
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Dec 12, 2017 at 4:53 history answered fedja CC BY-SA 3.0