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Sequential ambiguity

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In a specific sequence to create,
a1 has the elements x1 and y1,
a2 has the elements x2 and y2,
a3 has the elements x3 and y3,

The relationship between each term cannot be bijective, however it has a bounded range of finite whole numbers.

Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be such that after the sequence has been created, if you are given x3,y3,x2 and y1, then x1 and y2 can be determined i.e y2 = g(x2,x3)

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Solution Summary

This shows how to create a rule for a sequence that meets specified characteristics.

Solution Preview

I will use the notation x_n for x sub n.

Let's define y1 to be any positive integer, y_(n+1)=y_n + 1 (for instance y_n is 2,3,4,5,...) and x1=1, then define:

x_n=x_(n-1)+100 modulo y_n (so f(x,y)=x+100 mod y). (Just in case you do not know, x modulo y, or x mod y, means the reminder ...

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