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Gaps in sequantial list. 
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#1
Feb2012, 02:14 PM

P: 2

If I have a sequence 1,2,3,.. 1000. I can find a gap by summing up and subtrating from the sum of 1.. 1000 (usually with a known formula like n x (n+1) / 2 but with processing power I can just add 1 ... 1000 with a computer program).
If there is a two number gap, I can add squares as well and so have two equations with two variables SumOfOneTo1000  SumOfListWithGaps = x + y  Equation 1 SumOfOneSquareTo1000Sequare  SumOfSquaresFromListWithGaps = sqr(x) + sqr(y)  Eq 2 Now I have two equations and two unknown and I can simplify that into a quadratic equation with two roots. The roots are x and y. So I can a 2 number gap as well. How far can I go with this logic meaning with cubes and 3 gaps etc. What category does this problem fall under, is it information theory? thanks for your help. 


#2
Feb2012, 03:39 PM

P: 894

You are correct, that you can form n equations of n unknowns of the form:
[tex] A_(1)^(i) + A_(2)^(i) + ... A_(n)^(i) = X_(i) [/tex] i = {1,2,...,n}. But equations with i > 3 would fall in the category of higher algebra and would be difficult to solve. 


#3
Feb2012, 08:15 PM

Sci Advisor
P: 3,313

"Diophantine Equations" is the relevant mathematical topic, not "Information Theory". Information Theory takes place in a setting where there are probability distributions. 


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