Function of the following sequence I feel like this should be obvious for me, but I am not understanding this one.
Given: 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,..., I need to find a function for this. Thank you.

The On-Line Encyclopedia of Integer Sequences gives several formulas, including
$$
a_n=\left\lfloor\frac{1}{2}+\sqrt{2n}\right\rfloor
$$
The main point is that the sequence changes values at positions $1,2,4,7,11,\dots$, which is the sequence of triangular numbers $0,1,3,6,10,\dots$ shifted $1$ and these triangular numbers are given by $\frac{k(k-1)}{2}$. Hence the sequence of positions where the original sequence changes values is given by $j_k=\frac{k(k-1)}{2}+1$, $k=1,2,\dots$.
So the original sequence is given by $a_n=k$ if $j_k \le n < j_{k+1}$.
