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\section{Introduction}  Introduce the transform $T$ on a number $N$, in base $10$.  Say, $N=3024$, then the unique prime representation is $2^4×3^3×7$, and we can write a new number $T(3024)=22223337$. Repeating, we have $3×61×121439$ and $T^2(3024)=361121439$, again $3×7×43×399913$, giving $T^3(3024)=3743399913$. etc.  \begin{equation}  \begin{array}{|c|c|c|c|c|}  \hline  N & T(N) & T^2(N) & T^3(N) & T^4(N) \\  \hline  1 & 1 \\  2 & 2 \\  3 & 3 \\  4 & 22 & 211  5 & 5 \\  6 & 23 \\  7 & 7 \\  8 & 222 & 2337 & 31941 & 33371313 \\  \hline  \end{array}  \end{equation}