WARNING!!! MATHEMATICAL CONTENT!!!
The Hailstone sequence is the sequence defined as
If a(n-1) is odd, a(n)=3*a(n-1)+1, and
if a(n-1) is positive, a(n) = a(n-1)/2
Unfortunately I don't have subscripts at my disposal, so the function/sequence bleedover will have to suffice.
While it has yet to be proved, it is thought that the hailstone sequence converges to 1 for any starting number a(n). I was interested in the number of steps it took to reach one. For instance, starting number 2 obviously takes 1 step, and 4 takes 2. 3 takes 8 steps, while a starting number of 5 only takes 6. The graph then displays on the X-axis the starting number, and on the Y-axis the number of steps (for lack of a better word... perhaps "iterations"?) it takes to arive at one. I'll admit I stole the idea for such a graph from Wikipedia, but they only went up to 9,999, so I consider myself the victor, even more so if Excel could have more than 16384 columns, which my buddy pointed out is 2^14! He's a computer science major, so a more sophisticated graph may be forth coming.
On another note, a Saturday morning impromptu math class (a full 6 days of quality education for a 5 day price!) to learn about mathematical induction was scheduled. I am most excited!
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