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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 …
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 …
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, …