
EXAMPLE

The sequence starts (2, 1, 0, 2, 2, 2, 1, 0, 2, 2, 1, 2, 2, 0, 1, 0,...)
Instead of underlining terms, we will put parentheses around the terms we want to emphasize:
a(1) = 2 produces parentheses around a(1 + 3 = 4):
2, 1, 0, (2), 2, 2, 1, 0, 2, 2, 1, 2, 2, 0, 1, 0,...
a(2) = 1 produces parentheses around a(2 + 2 = 4), which is now already done. Then,
a(3) = 0 produces parentheses around a(3 + 1 = 4), which is already done. Then,
a(4) = 2 produces parentheses around a(4 + 3 = 7):
2, 1, 0, (2), 2, 2, (1), 0, 2, 2, 1, 2, 2, 0, 1, 0,...
a(5) = 2 produces parentheses around a(5 + 3 = 8):
2, 1, 0, (2), 2, 2, (1), (0), 2, 2, 1, 2, 2, 0, 1, 0,...
a(6) = 2 produces parentheses around a(6 + 3 = 9):
2, 1, 0, (2), 2, 2, (1), (0), (2), 2, 1, 2, 2, 0, 1, 0,...
a(7) = 1 produces parentheses around a(7 + 2 = 9), which is already done. Then,
a(8) = 0 produces parentheses around a(8 + 1 = 9)  already done. Then,
a(9) = 2 produces parentheses around a(9 + 3 = 12):
2, 1, 0, (2), 2, 2, (1), (0), (2), 2, 1, (2), 2, 0, 1, 0,...
a(10) = 2 produces parentheses around a(10 + 3 = 13):
2, 1, 0, (2), 2, 2, (1), (0), (2), 2, 1, (2), (2), 0, 1, 0,...
a(11) = 1 produces parentheses around a(11 + 2 = 13)  already done. Then,
a(12) = 2 produces parentheses around a(12 + 3 = 15):
2, 1, 0, (2), 2, 2, (1), (0), (2), 2, 1, (2), (2), 0, (1), 0,...
a(13) = 2 produces parentheses around a(13 + 3 = 16):
2, 1, 0, (2), 2, 2, (1), (0), (2), 2, 1, (2), (2), 0, (1), (0),... and so on.
We see in this small example that the parenthesized terms reproduce the initial sequence:
(2),(1),(0),(2),(2),(2),(1),(0),...
The same is true for the subsequence of nonparenthesized terms:
2, 1, 0, 2, 2, 2, 1, 0,...
