I want to search and replace each occurrence of a certain pattern with a decimal number which begins at 1 and increments by one for each match.

I can find similarly worded questions that turn out not to be about incrementing a counter but modifying each match by a fixed amount. Other similar questions are about inserting line numbers rather than an incrementing counter.

Example, before:

#1
#1.25
#1.5
#2

After:

#1
#2
#3
#4

My real data has a lot more text all around the stuff I want to re-number.