|
EXAMPLE
|
Nested interval sequences NI(k/m) for m = 41:
NI(1/41) = (41, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...),
NI(2/41) = (20, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, ...),
NI(3/41) = (13, 3, 1, 1, 4, 2, 2, 20, 1, 1, 1, 2, 2, 1, 1, 1, 2, ...) ~ NI(2/41),
NI(4/41) = (10, 1, 2, 1, 1, 8, 1, 1, 8, 1, 1, 8, 1, 1, 8, 1, 1, 8, 1, 1, ...),
NI(5/41) = (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, ...).
Any further NI(k/41) is equivalent to one of the above, e.g., NI(40/11) = (1, 1, 1, 1, 1, 4, 2, 2, 20, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, ...) ~ NI(2/41).
Thus, the number of equivalence classes is 4 (represented by 1/41, 2/41, 4/41 and 5/41), so that the fractility of 41 is 4.
|