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Consider the following sequence:

$(2,) 0, 1, 2, 2, 1, 1, 2, . . .$

Which digit comes next? How many digits can we predict until we encounter a digit we cannot predict?

There is a perfectly elegant non-mathematical solution to this problem!

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    $\begingroup$ Please see: Number-Sequence Puzzles: What (Not) to do $\endgroup$ – Beastly Gerbil Jan 14 '17 at 12:32
  • $\begingroup$ I'm pretty sure this is not an OEIS sequence! $\endgroup$ – anon Jan 14 '17 at 12:41
  • $\begingroup$ take a look at the other answer given, it applies more to this puzzle $\endgroup$ – Beastly Gerbil Jan 14 '17 at 12:41
  • $\begingroup$ Thanks for your feedback! Though it shouldn't be too ambiguous anymore. Also I provided extra context by stating there is a certain amount of digits we can know, and after that comes (at least one) digit we cannot know $\endgroup$ – anon Jan 14 '17 at 12:45
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    $\begingroup$ You're welcome! Welcome to puzzling btw, you might want to check out the tour to learn a bit more, or check out the highest voted questions $\endgroup$ – Beastly Gerbil Jan 14 '17 at 12:47
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I doubt this is the right answer but perhaps it's in the right direction? I'm not sure what the two in brackets is but this looks similar to

the Kolakoski Sequence (http://oeis.org/A000002)

Which means the next number would be

1

But if that were the case then there wouldn't be any point where we couldn't predict the next number, and you said it wasn't in the OEIS. Maybe something similar though.

Could we get some clarification on the (2) at the beginning of the sequence and maybe a few more numbers and I'll update my answer?

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The next is:

2,

for the reason that the sequence is:

2, (the number starting us off) indicating the start of the sequence, followed by 0, 1, 2, and then another 2, starting the next sequence, meaning that we can predict that the sequence will reach ...2,9,1,2 where the next number is uncertain because it could roll over to 2,10 or if limited to single digits, could roll over to 3,0,1.... etc.

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