Pattern Recognition

Try the Artificial Intelligence forum.

Here''s some logic on a method of pattern recognition:
The numbers 1, 4, 9, 16, 25... are squares. You can use the difference between each number, and the differences between those numners, and so on...

1   4   9   16  25
  3   5   7   9
    2   2   2
 

The third line will be all twos, so you can assume that it will continue that way...

1   4   9   16   25
  3   5   7   9
    2   2   2   2   2   2
 

Then you can add the 9 in the second row to 2 and get 11...

1   4   9   16  25  36
  3   5   7   9   11
    2   2   2   2...
 

This is the method I use. I''m even working on a program that will give you possible formulas from given patterns with this.



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Here comes the Thnikkaman!

That property comes from the fact that d^2(x^2)/(dy)^2 = 2. In fact any polynomial with only non-negative, integer coefficients will have an nth derivative whose value is constant. What about other functions that have no such property, such as f(x) = 1/x, or f(x) = e^x?

Cross post. Closed.