The Collatz conjecture says that you will always eventually reach the number 1. This conjecture has been tested to hold true for all starting numbers up to 87 x 260 but currently, no one has been able to mathematically prove that it holds true for any starting integer! For example, starting with the number 6, we get the numbers 6, 3, 10, 5, 16, 8, 4, 2, 1. These sequences are known as hailstone sequences. Write a program hailstones.py that prints all hailstone sequences with starting numbers from 1 to N and prints the number that has the longest hailstone sequence. The value of N is must be a positive integer obtain from standard input. Sample Program Input/Output The user inputs are appended by # and not part of the specification.

The Collatz conjecture says that you will always eventually reach the number 1. This conjecture has been tested to hold true for all starting numbers up to 87 x 260 but currently, no one has been able to mathematically prove that it holds true for any starting integer! For example, starting with the number 6, we get the numbers 6, 3, 10, 5, 16, 8, 4, 2, 1. These sequences are known as hailstone sequences. Write a program hailstones.py that prints all hailstone sequences with starting numbers from 1 to N and prints the number that has the longest hailstone sequence. The value of N is must be a positive integer obtain from standard input. Sample Program Input/Output The user inputs are appended by # and not part of the specification.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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I am what you call a perfectionist. I always strive for perfection, and I appreciate everyone and everything that is perfect. That is why I have recently acquired an appreciation for perfect numbers! I absolutely need to know which numbers from 1 to 1000 are considered perfect. From what I recall, a perfect number is a positive integer that is equal to the sum of all its divisors other than itself. Example: 6 is a perfect number because the divisors of 6 other than itself are 1, 2, and 3, and 1 + 2 + 3 = 6. c++ code
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1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16
A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors. The first perfect number is 6, because 1, 2 and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: (1 + 2 + 3 + 6) / 2 = 6. Write a program to display the of sum all perfect numbers found in the first 1000 integers.
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