[math-fun] Khinchin - Collatz connection??

There are 356033 integers within 41 Collatz (#/2 | (3#+1)/2) steps of 1. 356033/(4/3)^41 = 2.685357138639965 . . . 843774/(4/3)^44 = 2.684860516180538 . . . 63149973/(4/3)^59 = 2.685268450566904 . . . 112268898/(4/3)^61 = 2.685322969193732 But N@Khinchin = 2.685452001065306 (Thank Julian for the 4/3.) Does anyone recall an objection that the usual definition isn't really the expected geometric mean because its derivation assumes consecutive partial quotients are independent? Is there a "CorrectedKhinchin"? https://en.wikipedia.org/wiki/Khinchin%27s_constant and http://mathworld.wolfram.com/KhinchinsConstant.html say flatly No. (My Finch is on loan.) --rwg (EWW: In (8), the ln k belongs in the exponent.) Happy 8th, Gabriel!