Re the link to the wiki and its introductory paragraph: If you ask yourself why the 2nd part of the original Collatz function is: c(2k+1) = 3k+2 the reason

Re the link to the wiki and its introductory paragraph: If you ask yourself why the 2nd part of the original Collatz function is: c(2k+1) = 3k+2 the reason is that: 3x+1 applied to (2k+1) is 6k+4 which can immediately be divided by 2 and results in 3k+2.