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).(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Gaps in sequantial list.

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