The 3n+1 Problem & Beatty Sequences

[Joe Horn]

Some of you old timers might remember that the famous "3n+1 Problem" (aka the "Collatz Conjecture") was called "Ulam's Conjecture" in many issues of the PPC Journal back in the heyday of HP calculators.

By any wild chance, have any of you played with the 3n+1 Problem long enough to have noticed that the parity sequences of T(n) are identical to the finite differences of the Beatty Sequence based on log(3)/log(2)? Or have I discovered something new? I haven't seen it even after several months of searching, and even attempting to read some unreadable papers by one of the biggest experts on the 3n+1 Problem, Jeff Lagarias.

I'd get a wider audience at comp.sci.math and other places, of course, but I know that some of you have played with 3n+1 for many years, armed with programmable HP calculators, so I'm taking a chance that somebody here might have run across this identity already. Thanks in advance.