Revision 95df7d02-6f4b-4719-9826-70dbdeca9274 - Code Golf Stack Exchange

# [05AB1E], 34 bytes

Uses [Jonathan's mathematical insight](https://codegolf.stackexchange.com/a/180263/47066) that `ceil(n/3+3)` = `floor((n+8)//3)+1`

 ŽJćG8+‚2L>÷>NsÖ…™Ázz'ÒÖ‚×JNIв‚õKн,

[Try it online!][TIO-jsluua85]

[05AB1E]: https://github.com/Adriandmen/05AB1E
[TIO-jsluua85]: https://tio.run/##yy9OTMpM/f//6F6vI@3uFtqPGmYZ@dgd3m7nV3x42qOGZY9aFh1urKpSPzwJxJ11eLqXn@eFTSDWVu8Le3X@/zc0AAA "05AB1E – Try It Online"

**Explanation**

 ŽJćG # for N in [1 ...5001)
 8+‚2L>÷> # push [input//2+1, (input+8)//3+1]
 NsÖ # check each if N is divisible by it
 …™Ázz # push "fizz"
 'ÒÖ # push "buzz"
 ‚ # pair
 × # repeat a number of times corresponding to the result of the 
 # divisibility test
 J # join to string
 NIв‚ # pair with N converted to base <input>
 õK # remove empty string
 н, # print head of the remaining list