perplexus.info :: Just Math : Minimizing ones

Minimizing ones (Posted on 2024-03-20)

For each positive integer n, let k(n) be the number of ones in the binary representation of 2023 * n.
What is the minimum value of k(n)?

Bonus: Same question for 2024*n.

Source: Putnam 2023

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Findings

| Comment 1 of 4

I checked values for n up to 1 million and by brute force found:

The smallest solution for k(n, 2023) I found was:

4: 33175*2023 100000000000001000001000001

The smallest solution for k(n, 2024) I found was:

3: 269397*2024 100000100000000000000000001000

But I cannot be certain these are the absolute minimum values.

Posted by Larry on 2024-03-20 13:02:32

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