19.1.19

Dreaming of Collatz Exit Points

A few years ago I talked about Collatz exit points. Some Collatz exit points are reached a lot more frequently than others.  In fact, it appears that most integers reach only one such point.

Here are the first few Collatz exit points: 5, 21, 85, 341, 1365, 5461, 21845, 87381, 349525, 1398101, 5592405, 22369621, 89478485, 357913941, 1431655765, 5726623061, 22906492245, 91625968981, 366503875925, 1466015503701, 5864062014805, 23456248059221, 93824992236885, 375299968947541

Note: I call them Collatz exit points because for each ai in the set above 3*ai + 1 = 2i+1

As I already mentioned here there are only 3 odd integers below 100, for which 5 is not a Collatz exit. Below 200 there are also only 3, below 300 there are also only 3.

It seems 5 is the most commonly occurring Collatz exit point for all odd integers below 1000.

What about below 10000?

What about below 100000?

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