Slash chords which use a note that is a part of the main chord as the bass note are called inversions. Common open slash chords are:
C/E: 032010 or XX2010
E/G#: 4XX454 - weak
F/G: XXX011 or 120011 if you are elastic enough
5-string pattern for third in bass:
Find the bass note (third), bar two frets lower, play X20003 (where 0 is your finger) or X2000X. For a funky (but incorrect) sound, play X20000 which is strictly G6/B (or transposition thereof).