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Where would I begin if I wanted to develop an algorithm that maps consecutive whole numbers to a long list of unique sets of whole numbers. For example:

0 = {0, 0, 0}  
1 = {0, 0, 1}  
2 = {0, 0, 2}  
3 = {0, 0, 3}
4 = {0, 0, 4}
5 = {0, 0, 5}
6 = {0, 0, 6}
7 = {0, 0, 7}  
8 = {0, 0, 8}  
9 = {0, 0, 9}  
...
29436 = {19, 43, 11}
29437 = {19, 43, 12} 
29438 = {19, 43, 13}
29439 = {19, 43, 14} 
29440 = {19, 43, 15}
29441 = {19, 43, 16} 
29442 = {19, 43, 17}
29443 = {19, 44, 0}  
29444 = {19, 44, 1}  
29445 = {19, 44, 2}  
29446 = {19, 44, 3}  
...
64362 = {78, 5, 0} 
64363 = {78, 5, 1} 
64364 = {78, 5, 2} 
64365 = {78, 5, 3} 
64366 = {78, 5, 4} 
64367 = {78, 5, 5} 
64368 = {78, 5, 6} 
64369 = {78, 5, 7}

When a whole number (number to the left of = sign) is input, the algorithm should return the set of numbers assigned to the whole number. The set of numbers should be considered to be completely random. The list of number sets will be quite long but the exact amount of number sets is known. Is this possible? Is machine learning needed for this? Does there already exist an algorithm that can explain these relationships?

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    Given that 29436 = {19, 43, 11}, if we rewrite this as 19x + 43y + 11 = 29436, what are the values for x and y? – Robert Harvey Oct 14 '19 at 23:47
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If the sets of numbers are essentially random, then no, not beyond general compression algorithms. There's a fundamental limit on how much you can compress information - see Kolmogorov complexity. (https://en.wikipedia.org/wiki/Kolmogorov_complexity)

If the sets are themselves generated by an algorithm, or contain particular patterns, then it might be possible to develop a compression algorithm particularly suited to that data - although it would still be subject to a lower-bound on how small the "keys" could be.

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  • I see. Well the numbers in the set are not completely random actually. They are being generated by an algorithm that finds combinations of numbers that add up to a specific value. The issue is, while the radix of the left most number will always be 320, radix of the number second from the left changes at seemingly random places. the number third from the left changes also and way more frequently. So I thought in my question I would just call it random but I suppose some pattern might could be deciphered. Are there algorithms that do that? Find patterns in data in that way? – comp1201 Oct 15 '19 at 0:32

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