Print the Super Collatz numbers
Python 2, 104 bytes

c=lambda x:x&gt;1and 1+c([x/2,x*3+1][x%2])
lambda n:[1]+[x for x in range(2,n)if c(x)&gt;max(map(c,range(x)))]

c is a helper function that calculates the Collatz distance for a given integer. The unnamed lambda is the main function, which computes the super Collatz numbers up to (but not including) the input.