What do you think about this descent for black? How would you respond as white?

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[go]$$Bcm1
$$ ------------------------+
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$$ . . . . . X . . . O . . |
$$ . . , . . . . O , X 1 . |
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$$ . . . . . . . . . . . . |[/go]

q16 and then black should probably play r13 and it reverts to the more common joseki where black plays r13 first.

In the game I played black responded this way:

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[go]$$Bcm1
$$ ------------------------+
$$ . . . . . . . . . . . . |
$$ . . . . . . . 3 . . . . |
$$ . . . . . X . . . O . . |
$$ . . , . . . . O 2 X 1 . |
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$$ . . . . . . . . . . . . |[/go]

If white connects here it seems worse than the other joseki

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[go]$$Bcm1
$$ ------------------------+
$$ . . . . . . . . . . . . |
$$ . . . . . . . 3 . . . . |
$$ . . . . . X . . 4 O . . |
$$ . . , . . . . O 2 X 1 . |
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$$ . . . . . . . . . 5 . . |
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$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |[/go]

I was thinking about some kind of sacrifice strategy, but I'm not sure...

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[go]$$Bcm1
$$ ------------------------+
$$ . . . . . . . . . . . . |
$$ . . . . . . . 3 . . . . |
$$ . . . . . X . . 5 O 4 . |
$$ . . , . . . . O 2 X 1 . |
$$ . . . . . . . . . 6 7 . |
$$ . . . . . . . . . 8 9 . |
$$ . . . . . . . . . 0 . . |
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$$ . . , . . . . . , . . . |
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . . . . |[/go]

Yes taking the outside thickness is a good idea, but play 4 at 6 directly, it's a difference of almost a move as black will need to come back and cut and then you can play a better move than dieing in gote in the corner.

I would just answer at P18 and make miai of S17 and L17. But the variation you give is possible too. Hane at 6 directly is better as uberdude says. Because after the cut, W can descend to R18 to make better use of the corner aji.