Unbeknownst to the people on Earth, an alien invasion

Unbeknownst to the people on Earth, an alien invasion has been going
on for years, setting certain genetic markers in order to brainwash them
to do the alien’s bidding. Recently, this plot was discovered and
scientists are now rushing to find out how prevalent this problem is.
They have developed an oddly specific test based on the genetic
markers that the aliens use for their mind control.
This test involves putting the genetic markers in sorted order and
checking whether, for sufficiently many indices, the value at that index is
too close to said index, indicating that it was artificially set. If a person is
being controlled by the aliens, we aim to break the aliens’ influence by
reverting one of the genetic markers. To make it harder for the aliens to
counteract this procedure, we need to pick a random genetic marker
that they modified.
Your job is to help write the required algorithms to perform these tasks
and save the human race, before all hope is lost! Good luck! The fate of
humanity rests on your shoulders…