What is hailstone sequence?
It involves a sequence of numbers called a Hailstone sequence. It is called this because the numbers go up and down again. For example: 20 – 10 – 5 – 16 – 8 – 4 – 2 – 1 Hailstone Sequences follow these rules: If a number is even, divide it by 2 If a number is odd, multiply it by 3 and add 1.
What is the longest hailstone sequence?
A. The longest hailstone sequence is for the number 77031 whose length is 351.
What is 3n1 sequence?
The rule for creating the sequence is to start from some positive integer, call it n , and to generate the next term of the sequence from n , either by halving n , whenever n is even, or else by multiplying it by three and adding 1 when it is odd. The sequence terminates when n reaches 1.
Why are there hailstone numbers?
The sequence of numbers involved is sometimes referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.
Why the hailstone numbers are called?
Why is the hailstone sequence called that?
Sequences of integers generated in the Collatz problem. Such sequences are called hailstone sequences because the values typically rise and fall, somewhat analogously to a hailstone inside a cloud.
What is each number in a sequence called?
term
Each number in a sequence is called a term . Each term in a sequence has a position (first, second, third and so on). For example, consider the sequence {5,15,25,35,…} In the sequence, each number is called a term.
What is the sequence for 2n 1?
So the first 5 terms of the sequence 2 n 2 + 1 are 3, 9, 19, 33, 51.
What is the hailstone sequence for the number 27?
hailstone ( N,[ N | S]) :- 1 is N mod 2, N1 is (3 * N) + 1, hailstone ( N1, S). 2. Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1.
How do you find the hailstone sequence?
The Hailstone sequence of numbers can be generated from a starting positive integer, n by: If n is 1 then the sequence ends. The (unproven) Collatz conjecture is that the hailstone sequence for any starting number always terminates. This sequence was named by Lothar Collatz in 1937 (or possibly in 1939), and is also known as (the):
Do all hailstones eventually settle on the 4 cycle?
The question is whether every hailstone sequence eventually settles on the 4, 2, 1 cycle, no matter what starting value you use. Experiments certainly suggest that they all do. Computers have checked all starting values up to 5 x 2 60, a number that is 19 digits long, and found that the 4, 2, 1 cycle eventually appears.
How many elements are in a hailstone?
Hailstone (27) has 112 elements: [27, 82, 41, 124., 8, 4, 2, 1] Longest sequence starting under 100000 begins with 77031 and has 351 elements. -module( hailstone). -import( io).