If i wanted to covert 267 into Alternating between base 2 and 3 Bijective numeration here's how I would achieve it quickly.
Fist I divide my number by 2 with remainder.
so 267/2 = 133 remainder 1
I log the remainder 1
Now I divide by 3 with remainder
133/3 = 44 remainder 1
I log the 1 and this time divide the output by 2
44/2 = 22 remainder 0
Instead of 0 I log 2 and minus 1 from the output as to count without the 0
so 21/3 = 7 remainder 0
I log 3 and mius 1 from 7
6/2 = 3 remainder 0
I log 2 and minus 1 from the output 3
2/3 = 0 remainder 2
I log 2 and am now at 0 so I stop there.
What I have logged is (1,1,2,3,2,2)
Now I reverse what I have logged and 267 = 223211 in my strange alternating base.
You can determine if some of the time you can have a 0 or can't by simply not minusing 1 from the output and changing the 0 remainder to the divisor number and instead simply logging 0.