the c major scale on guitar

on my Eagle SI-30 BK electric guitar there are 22 frets.
the c major scale consists of the following barre chords:
0 5 10 12 17 22
0 5 10 12 17 22
0 5 10 12 17 22
0 5 10 12 17 22
0 5 10 12 17 22
0 5 10 12 17 22

so to me it looks like the pattern is this:
if the starting point is fret 0 (zero, open, no fingers at all on the frets)
it increases with 5 to get the next barre
it increases again with 5 to get the next one after that
it increases with 2 after that to get the next one
then starts again with increasing with 5
increasing with 5
then increasing with 2 (if there were more frets after the 22ndth fret)
so the pattern is:
5, 5, 2 (repeat)