How to calculate hailstone sequence?

How to calculate hailstone sequence?

The Hailstone sequence of numbers can be generated from a starting positive integer, n by:

1. If n is 1 then the sequence ends.
2. If n is even then the next n of the sequence = n/2.
3. If n is odd then the next n of the sequence = (3 * n) + 1.

What is Hailstone sequence in Python?

A hailstone sequence is a series of numbers that increase and decrease while following a pattern and eventually end when a repeating pattern is found.

What is hailstone numbers?

Sequences of integers generated in the Collatz problem. 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.. Pickover, C. A. “Hailstone Numbers.” Ch. …

Why is it called Hailstone sequence?

Hailstones do this – they start in a cloud as drops of rainwater, then they are pushed higher in the atmosphere by wind where they freeze, sometimes sev- eral times, before eventually falling back to Earth. The number sequences are called hailstone sequences because they go up and down like hailstones.

What is a hailstone conjecture?

The conjecture is that no matter what value of n, the sequence will always reach 1. 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.

Is Python a happy number?

A number is said to be happy if it yields 1 when replaced by the sum of squares of its digits repeatedly. If this process results in an endless cycle of numbers containing 4, then the number will be an unhappy number.

What is a hailstone in math?

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.

How to calculate the length of the hailstone sequence?

The same code we used to find the hailstone sequence can be used to calculate the length with few lines of changes in code. print(“Invalid input.”) print(“Invalid input.”) You have to find the seed having maximum lenght of the hailstone sequence for the hailstone sequences for all the numbers in range of given numbers.

What kind of numbers are called hailstone numbers?

Hailstone Numbers: The sequence of integers generated by Collatz conjecture are called Hailstone Numbers.

Which is the longest hailstone sequence in Rosetta Code?

Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124and ending with 8, 4, 2, 1 Show the number less than 100,000 which has the longest hailstone sequence together with that sequence’s length.   (But don’t show the actual sequence!)

When did Lothar Collatz name the hailstone sequence?

This sequence was named by Lothar Collatz in 1937   (or possibly in 1939),   and is also known as (the):   hailstone sequence,   hailstone numbers   3x + 2 mapping,   3n + 1 problem   Collatz sequence   Hasse’s algorithm   Kakutani’s problem   Syracuse algorithm,   Syracuse problem   Thwaites conjecture   Ulam’s problem