Adding to cells in a column

[SetofNine]

I have a column of numbers not in consecutive order or together. I want to add the number 1 to all the numbers in that column but not into the blank cells in between the cells that have numbers. There could be 6, 8, or 12 blank cells in between and there are 70 cells with numbers that need updating. Any help would be greatly appreciated.

 

[FDibbins]

I cannot think of a way to do this IN the cell, other than with VBA. copy/paste special/add will add 1 to the empty clls as well.

If you would consider using a helper column, this becomes simple...
=if(A1="","",a1+1)
copy down

Then, if needed, copy/paste values over the original data and delete the helper/formulas