Update2: Reset state to UNSOLVED

Why?

Anyway, I think what's confusing, at least to me, is that B=0; and I find what soonix said above is key (emphasis mine): "Counting B ... Z (without A) is like counting 1 ... 9 (without 0)."

How about this:

use feature 'state';
use Math::Fleximal;
sub getnext {
    state $num = Math::Fleximal->new("A",
        [qw/A B C D F G H J K L M N P Q R S T V X Y Z/]);
    do { $num=$num->add("B") }
        until $num->to_str!~/A/;
    return $num->to_str;
}
print getnext."\n" for 1 .. 1000;
__END__
B
C
D
...
Y
Z
BB
BC
BD
...
ZY
ZZ
BBB
BBC
...
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