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The Ludic Numbers

+4
−0

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.

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3 answers

+3
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Haskell, 51 49 bytes

-2 bytes thanks to Wheat Wizard

1:g[2..]
g(a:b)=a:g[d|(c,d)<-zip[1..]b,c`mod`a>0]

Try it online!

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Suggested golf (1 comment)
+2
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Python 3, 80 77 75 72 bytes

def f():
	yield 1;l=[*range(2,236425)]
	while l:yield l[0];del l[::l[0]]

Try it online!

Prints out the whole sequence. I did my best to get the biggest number that won't crash the program.

Golfed 3 bytes thanks to @Moshi's advice.

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list -> [*] (1 comment)
+2
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Sclipting, (UTF-16) 58 52 bytes

가匱❸增平갠下氫終要鈮貶⓶梴감⓶上❸乘殲終終并鈮掘增

Gives the nth ludic number, 0-indexed.

가
Start list of Ludics with 0
匱❹增平갠下氫終
Create a list of numbers from 2 to n+1 squared
要
While the list is truthy
  鈮
  Retrieve the Ludic number x (the first element)
  貶
  Decrement x
  ⓶梴감⓶上
  For i = 1 up to the length of the list
    ❸乘殲
    Remove the number at index x * i
  終
  End loop
終
End loop
并鈮掘增
Get the nth item from the list of Ludics and increment
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