The Hailstone Sequence

There is a sequence of numbers in mathematics that is sometimes known as the hailstone sequence. The German mathematician, Lothar Collatz, proposed that for any number it's possible to make a sequence of numbers that will eventually end in one by following a simple rule; if the number is even halve it by two, if it's odd times it by three and add one (e.g., starting with the number 5 the sequence would be 5 16 8 4 2 1).

The name hailstone comes from the way the pattern of numbers rise and fall, like a hailstone in a weather cloud before it drops to the ground.

Hailstone Sequence Exercise

Here's an opportunity to practice Java programming and writing loops. Create a program that can do the following:

  • calculate the hailstone sequence for a certain number. Remember, in order to get the next number just follow the simple equation:
     if the number is even : the next number = number / 2
     if the number is odd : the next number = (number * 3) + 1 
  • display the sequence so that every line you display has ten numbers.
  • display a sentence that says how many numbers there are in the sequence.

For example, if the number is 17 the output would be:

 17 52 26 13 40 20 10 5 16 8
 4 2 1 
 There were 13 numbers in the sequence.
 

The question is can your program calculate and display the numbers in the hailstone sequence for the number 125, as well as how many numbers there are in that sequence?

To get the most out of this question try and figure out the answer before looking at the sample solution below.

Hailstone Sequence Solution

The hailstone sequence for the number 125 is:

125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 There were 109 numbers in the sequence.

Here's a sample version of the program:

public class Hailstone {   public static void main(String[] args) {     int number = 125;     int calculation = 1;     System.out.print(number + " ");     while (number > 1)     {       if (number % 2 == 0)       {          //even number calculation          number /= 2;        }        else        {          //odd number calculation          number = (number*3) + 1;        }        calculation++;        //display nicely by wrapping around every 10th calculation        if (calculation % 10 == 0)        {          System.out.println(number);        }        else        {          System.out.print(number + " ");        }     }     System.out.println("\nThere were " + calculation + " numbers in the sequence.");   } }
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Leahy, Paul. "The Hailstone Sequence." ThoughtCo, Nov. 22, 2017, thoughtco.com/the-hailstone-sequence-2034025. Leahy, Paul. (2017, November 22). The Hailstone Sequence. Retrieved from https://www.thoughtco.com/the-hailstone-sequence-2034025 Leahy, Paul. "The Hailstone Sequence." ThoughtCo. https://www.thoughtco.com/the-hailstone-sequence-2034025 (accessed November 25, 2017).