Ruby, 34 29 26 2622 bytes
x=0;loop{p$.+=184while (x+=184)p$./629%2}
Quick explanation: this works because of the magic number 629. I noticed that the sequence starts repeating after the 629th element, and I tried to "improve" some existing answer, using only integer math. I found that the other "magic number" (0.29253) is actually 184/629.