
EXAMPLE

The sequence starts (6,5,4,3,2,1,0,6,6,6,6,6,6,6,5,4,3,2,1,0,6,6,...)
Instead of underlining terms, we will put parentheses around the terms we want to emphasize:
a(1) = 6 produces parentheses around a(1 + 7 = 8):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,5,4,3,2,1,0,...
a(2) = 5 produces parentheses around a(2 + 6 = 8), which is now already done. Then,
a(3) = 4 produces parentheses around a(3 + 5 = 8), which is already done. Then,
a(4) = 3 produces parentheses around a(4 + 4 = 8)  already done. Then,
a(5) = 2 produces parentheses around a(5 + 3 = 8)  already done. Then,
a(6) = 1 produces parentheses around a(6 + 2 = 8)  already done. Then,
a(7) = 0 produces parentheses around a(7 + 1 = 8)  already done. Then,
a(8) = 6 produces parentheses around a(8 + 7 = 15):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),4,3,2,1,0,...
a(9) = 6 produces parentheses around a(9 + 7 = 16):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),3,2,1,0,...
a(10) = 6 produces parentheses around a(10 + 7 = 17):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),2,1,0,...
a(11) = 6 produces parentheses around a(11 + 7 = 18):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),1,0,...
a(12) = 6 produces parentheses around a(12 + 7 = 19):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),0,...
a(13) = 6 produces parentheses around a(13 + 7 = 20):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),(0),...
a(14) = 6 produces parentheses around a(14 + 7 = 21):
6,5,4,3,2,1,0,(6),6,6,6,6,6,6,(5),(4),(3),(2),(1),(0),(6)...
a(15) = 5 produces parentheses around a(15 + 6 = 21)  already done. Then,
a(16) = 4 produces parentheses around a(16 + 5 = 21)  already done. Then,
a(17) = 3 produces parentheses around a(17 + 4 = 21)  already done.
Etc.
We see in this small example that the parenthesized terms reproduce the initial sequence:
(6),(5),(4),(3),(2),(1),(0),(6)...
The same is true for the subsequence of nonparenthesized terms:
6, 5, 4, 3, 2, 1, 0, 6, 6, 6, 6, 6, 6,...
