Question

The Collatz conjecture, also known as 3n + 1 conjecture, the Ulam conjecture or the Hailstone sequence or Hailstone numbers, was first stated in 1937 and concerns the following process:
1. Pick any positive counting number, n.
2. If n is even, divide by 2. If n is odd, multiply by 3 and add one.
3. If n = 1, stop; otherwise go back to step 2.

For example, if we start with 6, we get the sequence:

6, 3, 10, 5, 16, 8, 4, 2, 1.

The Collatz conjecture states that this process ALWAYS terminates at one, regardless of which positive integer for which we start the process. The conjecture has been checked by computer for all start values up to 3 x 253 (about 27,000 trillion) but no proof has been found. Paul Erdos, one of the most prolific mathematicians of recent and perhaps all time, said about the Collatz conjecture: "Mathematics is not yet ready for such problems." He offered $500 for its solution.

Investigate the efforts placed into finding a proof and why it is so elusive. Pick a few of your own starting numbers and report a Hailstone sequence of length twelve or more.

Answer 1

it there a question pending?

Answer 2

ohhhh i gotta edit the question uughhh give me a sec

Answer 3

Just to clarify: In Erdos's time, $500 was a lot.