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Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the sixth is the given number. That is, it is easy to find a rule so that any number can be the "next" in the sequence.

However, the simplest polynomial of order 4 is:

Un = (5n4 - 54n3 + 217n2 - 312n + 240)/12 for n = 1, 2, 3, ...

and, accordingly, U6 = 83.

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11y ago

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