Repeated Sampling

I have a question about repeated sampling. Let's say I am interested in the distribution of sample means. So what I would do is generate 10000 times a sample of size 1000 and look at the mean of each sample. Can I instead just take one sample of size 10000*1000 and then look at the mean of the first 1000 elements than from 1001 to 2000 and so on?