Collatz Sequence Maximums

To generate the values of the Collatz sequence, start with a number; if it is even, halve it, but if it is odd, triple it and add 1. Repeat the process. For example, if the sequence is 3, 10, 5, 16, 8, 4, 2 and finally 1. The Collatz problem (or problem) states that for any starting number the sequence eventually reaches 1. This is true at least for the many numbers that have been tried. Despite work since the 1930s, no proof for the general case is known. This Demonstration shows the maximums, highlighted in red, reached by the sequence for the first 100 integers.