jmc

Repeatedly dividing by 2, we find the next terms in the sequence to be 125000, 62500, 31250, 15625,... 15625 is no longer a multiple of 2, so when we divide by 2 again, we will not get an integer, nor will it be a multiple of 2. Thus, no number in the sequence after 15625 can be an integer. Thus, our answer is $\boxed{15625}$.