Empirical rule at different levels of significance in R

I am fairly new to R and I have a question that I've been stumped on.

I'm suppose to generate 6 samples from a standard normal distribution, with the sizes doubling every time I go to the next sample.

Then compute the percentage of data values less than Z_alpha/2. I must also print out the sample size and the percentages for each sample. My initial sample starts at n=20. I also need to record the findings for alpha=.05 and alpha =0.01

I'm assuming I have to use a for loop? With my n values starting from n=20 doubling from 40,80,160,320,640 which gives me the 6 samples I need?