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Given any 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 and the next is the given number. There are also non-polynomial solutions.

The simplest solution, in the form of a polynomial of order 3 is

Un = (3469n3 - 20661n2 + 37712n - 20346)/6 for n = 1, 2, 3, ... and accordingly, the next number is 14219.

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10y ago
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Q: What is the next number of the sequence 29 31 84 3657?
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