Banjo F chord (Double C)F major on the 5-string banjo: 0 2 0 3, and 6 more shapes

Frets, string 4 to string 1: 0 2 0 3 (open position)

1. String 4 (C): open, C
2. String 3 (G): 2nd fret, index finger, A
3. String 2 (C): open, C
4. String 1 (D): 3rd fret, middle finger, F
5. String 5, the short g: open, G, not in the chord

Sounds: C A C F  ·  F is F, A, C (1 · 3 · 5)

Found in: C major (IV), G mixolydian (♭VII), C mixolydian (IV), G dorian (♭VII), D dorian (♭III), C dorian (IV)

The 5th string: the short g adds the 9th over F, a colour rather than a clash.

Double C tuning: gCGCD, the short 5th string first, then strings 4 to 1.