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For questions about sequences of integers. References are often made to the online resource oeis.org.

5 votes

Sequences with integral means

Lucia already proved in a comment that the sequence stabilizes: at each step the mean decreases or stays the same, and once the sequence is longer than the mean the mean can no longer decrease. For t …
Noam D. Elkies's user avatar
15 votes

Distance among integer set

To simplify notation define $\delta(x,y) = |x-y|$. Here's an easier proof (using only Euclid) of the result in the answer that Seva posted: a finite set of positive integers closed under $\delta$ a ho …
Noam D. Elkies's user avatar
10 votes

Maximal number of edges and triangular cells for n points in a triangular lattice

You might have noticed that the difference between your two sequences is $0,1,2,3,4,5,6,7,8,\ldots$ and that the optimal configurations seem to be the same for both problems. This is true in general, …
Noam D. Elkies's user avatar