Strange result

Just playing around with values. I started seeing how large the set was of numbers which peak underneath a certain value under the Collatz map. For instance, the number 27 eventually goes to 1, but it goes through the number 4616 to get there. There are 1171 numbers below 4616 with such a property, which is quite surprising, as 4616 seems to be a rather dull number. However when you look at it base 3, a surprising pattern jumps out. Other numbers with large sets below which pass through them seem to have a similar pattern.

4616 = 2022222 in base 3

19682 = 222222222 base 3

47978 = 2102210222 base 3

Each of these values has hundreds of lower values which pass through it. There are other examples as well, and they all end in long sequences of 2s when looked at mod 3.