evidence of a correspondence between Mersenne prime exponents and stopping times in the Collatz conjecture

[Martin Doina]

I find empirical evidence of a correspondence between Mersenne prime exponents and stopping times in the Collatz conjecture. Through systematic computational analysis, I see that numbers whose Collatz sequences require exactly steps to reach 1—where is a Mersenne exponent—form structured clusters with distinctive mathematical properties. These clusters exhibit hierarchical branching patterns, digital root distributions, and scaling behaviors that reveal previously unknown connections between number theory and discrete dynamical systems.

https://zenodo.org/records/17589818

[Ruud H.G. van Tol]

See https://oeis.org/A100982/a100982.txt about dropping times,
specifically the "v2 + i*2^p2 --> v3 + i*3^p3" table. The 2^n-1 values
(1,3,7,15,...) turn up as v2. There is also a graphical view:
https://oeis.org/A100982/a100982.svg -- Ruud