Double peep problem: K16

This move - K16 (response to J15) - always puzzles me.
How to respond to it ?
Tried some variants - J16, K17, L15 - but none of them seem to work.
Is maybe J15 a bad move?

What do you think of these variations?

The first shows White connecting underneath; the second shows the connection on the side.

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Thanks.
Just kept looking in the wrong direction.

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I think K16 is a legit attack/probe by black in this shape to harass white (well, not really this exact shape, because I think black would normally need a stone at O17 for good follow-ups. P17 is a bit too far away.).
This harrassment would work even better if black has a stone at G15.

If white connects at J16, I think black’s usual follow-up is not 3. Playing directly at 5 would be the shape move.
In general, 3 is a bit crude, helping white to become really thick on the outside and hurting the G17 stone, but it may work in specific situations.
Another potential follow-up move for black is to attach on top at M16, which is usually played if black can make a large moyo on the right (which is not the case here).

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You can find some examples of this shape in Waltheri’s BTW:

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Rejoice! GoPro made a video specifically for you.

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