I was asked to create, if possible, a divergent sequence such that for every $n$ in $N$, it is possible to find '$n$' consecutive ones somewhere in the sequence.
I came up with the sequence: $\{1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4,...\}$.
Where the series can be thought of in blocks. I.e, in block $n=1$ $\{1\}$, in block $n=2$, $\{1,1,2,2\}$ and so on.
I am wondering if there is a way to write this sequence in a more succinct way.