Purposes of this assignment

• To familiarize you with IDLE
• To get you started programming in Python
• To teach you a little bit about functions

General idea of the assignment

In this assignment you will write a number of functions for testing characteristics of positive integers, plus one special function named main. Each function other than main will take a single positive integer as an argument, test whether it has some property, and return a value of either true or false.

Put your program on a file named number_personalities.py. Get a copy of the file number_personalities_test.py.

Details

The main() function

In the main function, define a variable limit = 100 and test each of the numbers 1 through limit, inclusive. Do not use the number 100 elsewhere; use the variable limit instead. This makes the program easier to change if you later want some limit other than 100.

The main function will call each of the other functions, for each of the numbers 1 through limit, to determine the properties of those numbers. It will then print out each number, one per line, along with a list of its properties (on the same line).

Your output should look approximately like this:

    1   composite, happy, triangular, square, not smug, honest
    2   prime, unhappy, not triangular, not square, smug, honest
    3   prime, unhappy, triangular, not square, not smug, honest
    4   composite, unhappy, not triangular, square, not smug, honest
    5   prime, unhappy, not triangular, not square, smug, dishonest
    . . .

The main function doesn't return a value. Each of the other functions is a predicate, that is, a function that returns True or False.

The is_prime(n) function

A positive number is prime if its only positive divisors are itself and one. For example, 7 is prime because it is evenly divisible by 1 and 7, but not by any number in between (in particular, it is not evenly divisible by 2, 3, 4, 5, or 6).

A positive number is composite if it is not prime. For example, 10 is composite because it is evenly divisible by 2 and 5; 12 is composite because it is evenly divisible by 2, 3, 4, and 6. As a special case, 1 is considered to be composite.

This function should return True if its argument is a prime number, and False otherwise. Similar statements hold for the other functions.

The is_happy(n) function

Repeatedly apply the following procedure to a number:

1. Square each of the digits of the number.
2. Add the squares together.

If by doing this you eventually get to 1, then the number is happy.

For example, if you start with 19:

• 12 + 92 = 1 + 81 = 82
• 82 + 22 = 64 + 4 = 68
• 62 + 82 = 36 + 64 = 100
• 12 + 02 + 02 = 1 + 0 + 0 = 1 and the number is happy.

If instead you get into an infinite loop, the number is unhappy. So if your program runs forever, the number is unhappy. This isn't a very useful test, however. Fortunately, every unhappy number will eventually get into this cycle:

4, 16, 37, 58, 89, 145, 42, 20, 4, ...

so if you get any one of these numbers, say 4, then you can stop and conclude that the number is unhappy.

The is_triangular(n) function

A triangular number is a number of the form 1 + 2 + 3 + ... + n, for some positive n. These numbers are called triangular because, if you have that many objects, you can arrange them in an equilateral triangle (see figure).

The first few triangular numbers are 1, 3, 6, 10, 15....

The is_square(n) function

The is_smug(n) function

A number is smug if it is the sum of two square numbers. The first few smug numbers are 2 (1+1), 5 (1+4), 8 (4+4), 10 (1+9), 13 (4+9), etc.

The is_honest(n) function

A number is dishonest if it "pretends" to be a square number, but isn't one. Specifically, n is dishonest if there is a number k such that n // k = k (using integer division), but k * k is not n. A number is honest if it is not dishonest.

Coda

At the end of your Python program (after all your function definitions), insert the following lines:

if __name__ == "__main__":
  main()

Due date

Turn in your one Python file to Canvas by 6am Thursday, September 3.