> ...although I just tested it, and the increment and 0-padding only work in non-interactive mode ='(

Works for me...

    $ echo $0 # determine current shell (alternative: "ps -p $$")
    bash
    $ echo {01..100..20}
    001 021 041 061 081

But note that `{x..y}` has a major limitation: it doesn't support variables. Example:

    $ n=5
    $ echo {1..$n}
    {1..5}
    # intended output: 1 2 3 4 5

The `for ((...))` syntax mentioned by @zazaulola supports variables (it works in bash and zsh).

For completeness, here is a POSIX sh approach that doesn't require `seq` (in fact I notice this is what your "Uber Fancy" version uses internally):

    i=1
    while [ "$i" -le 5 ]; do
        echo "$i"
        i="$((i+1))"
    done

(but note that `continue` won't work properly).