I find this (FFOSM) works in Open C

1st to 6th : E C G C G E or C, as you choose.

I tend not to play the 6th in this tuning, on FFOSM, anyway.

The do, re, mi, so run I play on the C strings in octaves - open ; fret 2nd ; fret 4th ; fret 7th.

Hope this helps.