Python Math: Print the first n Lucky Numbers

Last update on January 06 2025 13:41:24 (UTC/GMT +8 hours)

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.

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:

Python Code Editor:

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