Wolfram Language (Mathematica), 6058 bytes
(a={x=2};Do[While[Mod[Times@@a;Do[While@Mod[Times@@a,++x]==0];AppendTo[a++x]==0;AppendTo[a,x],#];a)&
Print given number of sequence members.
Based on the next statement from Wiki:
Another way of defining this sequence is that each element is the smallest positive integer that does not divide the product of all of the previous elements of the sequence.