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Any number that you choose can be the next number. It is easy to find a rule based on a polynomial such that the given numbers are as listed in the question followed by the chosen next number. 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.

Here, one possible solution is that all the numbers in even position are 6 and for those in the odd positions,

U(2n-1) = (n^2 - 16*n + 71)/8, for n = 1, 3, 5, 7, ...

and accordingly, the next term is 1.

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9y ago
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Q: What comes next with 7 6 4 6 2 6 1 6?
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