Hailstone numbers are the integers in sequences associated with the Collatz conjecture. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, .... Such sequences are called hailstone sequences because the values typically rise and fall, somewhat analogously to a hailstone inside a cloud.
While a hailstone eventually becomes so heavy that it falls to ground, every starting positive integer ever tested has produced a hailstone sequence that eventually drops down to the number 1 and then "bounces" into the small loop 4, 2, 1, ....
The hailstone trajectories for starting values 
, 2, ... form an irregular triangle whose 
th row is the trajectory beginning at 
and ending at its first occurrence of 1, provided that occurrence
exists. Reading the rows successively gives 1; 2, 1; 3, 10, 5, 16, 8, 4, 2, 1; 4,
2, 1; 5, 16, 8, 4, 2, 1; ... (OEIS A070165).
Different rows merge whenever their trajectories meet, so the triangle contains many
repeated tails.
