Hard Logic Sequence Puzzle

Complete the following series. It.s very logical:

1, 4, 5, 6, 7, 9, 11, __?




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A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

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Amazing Facts

No Solution

In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki