# Matrix sequence

While a one-dimensional sequence is represented by a list, a two-dimensional sequence (a sequence of sequences) can be represented by a matrix. Find the pattern behind the following sequence, where a section of the matrix with unknown coordinates is shown below.

$\begin{bmatrix} &\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ \dots& 1 & 5 & 3 & 7 & 1 & 9 & 5 & 13 & 3 &\dots\\ \dots& 4 & 7 & 2 & 5 & 8 & 1 & 10 & 19 & 4 &\dots\\ \dots& 1 & 5 & 9 & 13 & 2 & 6 & 10 & 14 & 3 &\dots\\ \dots& 4 & 1 & 6 & 11 & 16 & 21 & 2 & 7 & 12 &\dots\\ &\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ \end{bmatrix}$

The pattern is that the number in the $m$th row and $n$th column is
the number $n$, written in base $m$, reversed, and converted back into base 10. The section shown is the 2nd through 5th lines, 4th through 12th columns.
For example, the $4$th row, $11$th column would be calculated like this: $11_{10}=23_4\rightarrow32_4=14_{10}$