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Any number that you choose can be the nth number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by the chosen number in the nth position (n>4). There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.

A solution, based on a polynomial of order 2, is

U(n) = n^2 - 1.

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9y ago

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