Find the Next No.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211




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I am thinking of a five-digit number such that:
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What number I am thinking of?

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710 57735 34 5508 51 7718

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R | E | A | D

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Gamers

In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.