Formula for the total Hamming weight of the sequence of 1, 2, ..., n

Asked Apr 18 '23 at 16:53

Active Apr 19 '23 at 10:58

Viewed 25 times

This problem is fairly straightforward if log2(n) is a whole number as we can use a simply use:

n * log2(n)/2

however it miscounts when log2(n) isn't a whole number. My intuition is there should be a formula similar to this that works for all n but I'm having trouble finding it.

edited Apr 19 '23 at 10:58

asked Apr 18 '23 at 16:53

Lucas

I guess it is `for i from 1 to log2(n):` – Damien Apr 18 '23 at 17:36
1

And in this simple case, the result seems to be `n * log2(n)/2` – Damien Apr 18 '23 at 17:38

Formula for the total Hamming weight of the sequence of 1, 2, ..., n

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