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According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.

The simplest polynomial rule is

Tn = (103*n4 - 1242*n3 + 5201*n2 - 8670*n +4680)/24 for n = 1, 2, 3, ... and accordingly, the next number is 213.

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7y ago

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