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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. Here, for example, the answer could be

  • 2 : delete on digit from the left
  • -488 : Arithmetic progression, with Un = 1012 - 5*n
  • 0.28125 : Geometric progression with U1 = 512 and U(n+1) = Un*(3/128)
  • 4.78 (approx) : U(n+1) = 4*3*log(Un) where the logarithm is to base 2.
I could think of hundreds more which, in the right context, would make absolutely good sense.
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