Hard Logic Sequence Puzzle

Complete the following series. It.s very logical:

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




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I can prove why 1 = 2

* Lets say y = x
* Multiply through by x xy = x2
* Subtract y2 from each side xy - y2 = x2 - y2
* Factor each side y(x-y) = (x+y)(x-y)
* Divide both sides by (x-y) y = x+y
* Divide both sides by y y/y = x/y + y/y
* And so... 1 = x/y + 1
* Since x=y, x/y = 1 1 = 1 + 1
* And so... 1 = 2

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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