> each will only be lit for 1/42 of the time.
> 
> Exactly, I'll multiplex them one LED at a time

I'm pretty sure 2.38% duty cycle is not going to look very good. LEDs
will be on, but quite dim. You need only one LED and some s/w to test
that

(1) the refresh rate would have to be fairly high to cover all the LEDs
without flicker

(2) increasing the scan rate reduces the time each LED is serviced

(3) reducing the service time increases the current needed to make the
LED "brighter than normal" for persistence of vision to kick in for any
appreciable time. 97.6% 'off' time in fact

(4) PIC pins on their own cannot supply that much burst current

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