One could do something like:
B1 cell: =$A$1+ROW()
When one copies that cell, the value of ROW() (without any arguments) will have the value of the row it is on, resulting in the value of 1 for cell B1, 2 for cell B2, etc.
The problem is that if that section of the spreadsheet is relocated further on down on the page or on another page, ROW() might not be what one wants, but one might decide one would rather have ROW()-5 if one had inserted five rows before the desired row. Of course, relocating the value may also mean the absolute cell reference of $A$1 would also need changing.
ROW() can also take a cell reference, so one could code, for example,
=$A$1+ROW()+1-ROW($A$1)
and then if the sheet gets relocated to a different spot on the page, after correcting the absolute reference, one would get the correct values again.
I personally am not fond of that solution. I am one of those who would prefer using a column that starts with the value 1 and use a formula that adds 1 to it, e.g.,
C1 cell: 1
C2 cell: =C1+1
and then copy C2 down as far as needed.
Then one could use
B1 cell: =$A$1+C1
and copy that formula down as far as needed.