deletions | additions       diff --git a/Curious Mappings.tex b/Curious Mappings.tex  index 1fea9d1..8d6a816 100644  --- a/Curious Mappings.tex  +++ b/Curious Mappings.tex 
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Of course the operation that forms a reduction of series $S$ to $F$ does not have to be a sum, it may be any operation which is appropriate. A question is then, can such a device be used to generate important series from other series, to porvide a direct mapping between say the numbers $1,2,3,4,5...$ to the prime numbers $2,3,5,7,11...$?  To find such a mapping we know, if the column wer summed over, we are allowed a number of terms to form the final series element as the column adress minus one. In short, the first element of the series is one element from the matrix, the second the sum of two and so on. The ways to sum $n$ elements into a number much greater than $n$ is a problem, as there are many combinations, and perhaps only one is valid. However, any such direct mapping would have to be valid for small numbers as well as large, so it would be best to exhaust the possibilites for smaller elements and extrapolate the series upwards. So a short program was written to analyse these sums further. Here are some sequences...  \begin{equation}  \begin{array}{|c|c|c|}  \hline   f(i,j) & g(i,j) & N \\  \hline   j-i & j+i & 6,24,60,120,210,336,504,720,990,1320 \\  \hline   \end{array}  \end{equation}