I have a set of numbers:
$\begin{array}{r(22)}x \in \{ 1,& 2,& 3,& 4,& 5,& 6,& 7,& 8,& 9,& 10,& 11,& 12,& 13,& 14,& 15,& 16,& 17,& 18,& 19,& 20,& 21,& 22, \dotsc \} \\ p \in \{ 1,& 2,& 2,& 3,& 3,& 3,& 4,& 4,& 4,& 4,& 5,& 5,& 5,& 5,& 5,& 6,& 6,& 6,& 6,& 6,& 6,& 7, \dotsc \}\end{array}$
The first $x$ matches with the first $p$ and so on...
I am trying to find an equation that will give me the $p$ value given $x$, i have tried $p = \lceil (x-1)^{0.5} \rceil + 1$. It works for the first few values then stops...
Thanks