Found this Excel formula. Not sure if it's possible to use this to Excel formula as a model for a QuickBase formula, but I'll give it go.
A2 contains the Base 10 number
B2 contains the base number conversion (base 2 to 36)
C2 contains this formula:
=CONCATENATE(
IF(FLOOR(A2/$B$2^12,1)=0,"",IF(MOD(FLOOR(A2/$B$2^12,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^12,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^12,1),$B$2))),
IF(FLOOR(A2/$B$2^11,1)=0,"",IF(MOD(FLOOR(A2/$B$2^11,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^11,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^11,1),$B$2))),
IF(FLOOR(A2/$B$2^10,1)=0,"",IF(MOD(FLOOR(A2/$B$2^10,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^10,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^10,1),$B$2))),
IF(FLOOR(A2/$B$2^9,1)=0,"",IF(MOD(FLOOR(A2/$B$2^9,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^9,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^9,1),$B$2))),
IF(FLOOR(A2/$B$2^8,1)=0,"",IF(MOD(FLOOR(A2/$B$2^8,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^8,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^8,1),$B$2))),
IF(FLOOR(A2/$B$2^7,1)=0,"",IF(MOD(FLOOR(A2/$B$2^7,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^7,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^7,1),$B$2))),
IF(FLOOR(A2/$B$2^6,1)=0,"",IF(MOD(FLOOR(A2/$B$2^6,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^6,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^6,1),$B$2))),
IF(FLOOR(A2/$B$2^5,1)=0,"",IF(MOD(FLOOR(A2/$B$2^5,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^5,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^5,1),$B$2))),
IF(FLOOR(A2/$B$2^4,1)=0,"",IF(MOD(FLOOR(A2/$B$2^4,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^4,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^4,1),$B$2))),
IF(FLOOR(A2/$B$2^3,1)=0,"",IF(MOD(FLOOR(A2/$B$2^3,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^3,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^3,1),$B$2))),
IF(FLOOR(A2/$B$2^2,1)=0,"",IF(MOD(FLOOR(A2/$B$2^2,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^2,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^2,1),$B$2))),
IF(FLOOR(A2/$B$2^1,1)=0,"",IF(MOD(FLOOR(A2/$B$2^1,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^1,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^1,1),$B$2))),
IF(MOD(FLOOR(A2/$B$2^0,1),$B$2)>9,CHAR(MOD(FLOOR(A2/$B$2^0,1)-10,$B$2)+65),MOD(FLOOR(A2/$B$2^0,1),$B$2))
)