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Python Math: Print the first n Lucky Numbers

Python Math: Exercise-17 with Solution

Write a Python program to print the first n lucky numbers.

Lucky numbers are defined via a sieve as follows.
Begin with a list of integers starting with 1 :
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, . . . .
Now eliminate every second number :
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...
The second remaining number is 3, so remove every 3rd number:
1, 3, 7, 9, 13, 15, 19, 21, 25, ...
The next remaining number is 7, so remove every 7th number:
1, 3, 7, 9, 13, 15, 21, 25, ...
Next, remove every 9th number and so on.
Finally, the resulting sequence is the lucky numbers.

Following animation demonstrating the lucky number sieve. The numbers in red are lucky numbers.

lucky number sieve

Animation Credits: Celtic Minstrel

Sample Solution:-

Python Code:

n=int(input("Input a Number: "))
List=range(-1,n*n+9,2)
i=2
while List[i:]:List=sorted(set(List)-set(List[List[i]::List[i]]));i+=1
print(List[1:n+1])

Sample Output:

Input a Number: 10                                                                                            
[1, 3, 7, 9, 13, 15, 21, 25, 31, 33] 

Flowchart:

Flowchart: Print all permutations of a given string

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor:

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Next: Write a Python program to computing square roots using the Babylonian method.

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Python: Tips of the Day

Given each iterable to construct a tuple by adding an index:

>>> a = ['Hello', 'world', '!']
>>> list(enumerate(a))
[(0, 'Hello'), (1, 'world'), (2, '!')]

 





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