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How does this sequence end?

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1 3 1 2 2 8 3 3 1 4 3 0 5 3 1 6 3 0 7 3 1 8 3 . . . .?

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There are 39 digits total in the sequence, and the last digit is 1.

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2 9 3 1

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2 9 3 1

Not quite.

See Rainman's post for a strong clue.

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