Don't you be no square...

1871121171 is a 10digit number where
all consecutive 3digit numbers have
a sum-of-digits that is a square:
1+8+7 = 16
8+7+1 = 16
7+1+1 = 9
1+1+2 = 4
....and so on to:
1+7+1 = 9

What is the highest such 10digit number?

Easier than it appears to be!

9979979979

Mais oui!