Revision 46c38270-ff7d-48e4-87f6-b938436c0034 - Code Golf Stack Exchange

# [R], 173 bytes

<!-- language-all: lang-r -->

 function(b){Map(function(i)"if"((s=paste0("if"(i%%(b%/%2+1),"","Fizz"),"if"(i%%((b+11)%/%3),"","Buzz")))>"",s,(function(i){a=0
 while(i){a=c(a,i%%b)
 i=i%/%b}
 a})(i)),1:5000)}

[Try it online!][TIO-jsi9akcz]

Not sure whether a leading 0 is allowed (and extra characters for that matter), will change if needed

[R]: https://www.r-project.org/
[TIO-jsi9akcz]: https://tio.run/##TY9BasMwEEX3OoUYMMwQQSSHdGFQFll0lxPUXUjGogNGNpFDIcZnd@Q6DdnN430ezHUJdgm32IzcR/Q0XdyAL2YCDoCY7ODS2Gr8Qy4K9MW@KHeGFICCT77fIZ//Ev3OGMqLw@bPt9UTnTIk9Z6fnNXi94e7doMGncoFT4It54CfhZspO1KmOmqtaV5Cf0WWHGVZfZQkJyFl40aEOtbRWivPLrWgWEGGOgI9/fODkGNfpjJaf6um7zo3pNbCuiMxLw8 "R – Try It Online"