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Project Euler Problem 443 – GCD sequence

Spoiler Alert!
This blog entry contains content that might help you solve problem 443 of Project Euler. Please don’t read any further if you have yet to attempt to solve the problem on your own. The information is intended for those who failed to solve the problem and are looking for hints. It is posted not before the problem has a hundred solvers already.

Test Data

ng(n)
1028
100268
10002524
10422540
105201142
1062624152
10722993888
108203960692
1092663410132
101023307401380
1011206459479984
10122703351832210
101323626818288232