The Ludic Numbers are a sequence that pops up when you apply the sieve of eratosthenes to the natural numbers, completely removing the numbers every iteration.

Here is how they are generated:

The Ludic numbers start with the lists:

l = [1]
n = [2,3,4,5,6,7,8,9,10....]

Every iteration, we take the first element x in n, add it to the list, and remove every xth number in n, including x.

l = [1,2]
n = [3,5,7,9,11,...]

By repeating this process an infinite number of times, we can get the full list of Ludic numbers.

Challenge

For this sequence, you can

• Take an index $n$ and output the $n^{th}$ term, either 0 or 1 indexed.
• Take a positive integer $n$ and output the first $n$ terms.
• Output the whole sequence as an infinite list.

Testcases

1		1
2		2
3		3
4		5
5		7
6		11
7		13
8		17
9		23
10		25
11		29
12		37
13		41
14		43
15		47
16		53

The first 56 values can be seen here: A003309.

Reference implementations can be found at Rosetta Code.

Scoring

This is code-golf. Shortest answer in every language wins.

posted over 2 years ago

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10mo ago by trichoplax‭

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