It is a common way to defend, for White to play 1 and 3 like this for a bulge shape. But how to answer Black 4?
White 1 here is counter-atari: it defends against atari not by connecting up but by sacrificing. This is almost always the correct way to play here
After Black captures with 2, White can play atari at a or b, taking account of the overall position. Black then probably connects, rather than challenge to a big ko fight.
For White to connect with 1 here is an empty triangle of a very heavy kind. This is rarely a good play.
What happens now? White 1 and Black 2 are normal since Black cannot expect to fight a ko early in the game (no ko threats in the opening). Black will have a pincer stone at one of the points a to f. With a close pincer (a or b) White now usually connects solidly at p. with the aim of extending to the marked point. With the more distant pincers d and e White makes the trumpet connection at q for better shape (the other two pincers are rare in this pattern).