Yes, this is quite well known. See (e.g.) the third paragraph on Terrence Tao's blog here https://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-litt

Yes, this is quite well known. See (e.g.) the third paragraph on Terrence Tao's blog here https://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-littlewood-offord-theory-and-powers-of-2-and-3/ https://terrytao.wordpress.com/2011/08/25/the-collatz-conjec... For what its worth Tao is possibly the only person in the world I wouldn't be shocked to hear of making progress on the Collatz conjecture. He actually proved a pretty nice result on it recently https://arxiv.org/abs/1909.03562 https://arxiv.org/abs/1909.03562 but the technology employed doesn't seem strong enough to go beyond "almost all" statements.