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Given any number it is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.

The simplest polynomial of order 5 is

Un = (4n5 - 85n4 + 655n3 - 2255n2 + 3421n - 1710)/30 where n = 1, 2, 3, ...

Accordingly, the next number is 15.

However, I suspect that the answer that you are looking for is 6.

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10y ago
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Q: What number comes next 1 4 1 5 9 2?
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