hmmmmm........I'm guessing you are talking about a refinance transaction.
Depending on the timing of your closing, you may have a breather from payments but you're not really skipping any. Here's an example:
You have an existing mortgage with a payment due date of the 1st of April. The grace period is 15 days.
You schedule your refinance closing for the 10th of April. Even with the rescission period, the payoff will reach your mortgage lender before the end of the grace period so you don't make April's payment.
Your new lender collects interest from the disbursement date through the end of April and sets up your first payment due date on June 1st. You don't make a mortgage payment for either April or May.
In both cases, you are paying interest to each mortgage lender for everyday you are using their money, but those funds are being reconciled through the payoff and closing.
It's important to know that most mortgages have interest paid in arrears. That means the June payment for the new mortgage is actually paying interest for the month of May.
I hope this answer is somewhere near the basis of your query. It only covers two payments in the "skip" scenario and I confess I can't account for the four skip theory.