Incrementing in a group pattern

You could use some ROW() and INT() and MOD() formulas to do this, but I'd recommend just hardcoding a 1 in A1, A2, A3, and A4. Then the formula in A5 is =A1+1. Grab that formula and drag down as far as you wish.

Now I see you want a quick method as you can't drag it down. Not quite sure what you want, as there are many ways to quickly paste. In my example above, just copy A5, select the range where you want that formula to apply (using the shift key to quickly select an array of cells), then hit paste.