On November 14, 2017 our data on number of steps in Collatz sequence for Mersenne primes with the provisional index from 46th to 49th were included in OEIS as a comment to A181777. Prior to this A181777 contained information up to the 45th Mersenne prime only.
Below is a table with our data for all known Mersenne primes starting from the 43rd.
Mp # of steps to 1
As far as we know, full Collatz conjecture statistics for large Mersenne primes has never been published before and none of Mersenne primes above the 47th one (M43112609) has ever been tested for Collatz conjecture confirmation.
We continue to process our results and plan to present most important of them in the future.