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The Ludic Numbers[FINALIZED]
#3: Post edited
by
trichoplax
·
2023-06-19T10:25:29Z (over 1 year ago)
Add finalized tag now that the sandbox can be filtered to exclude tags
The Ludic Numbers[FINALIZED]
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 `x`th 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](http://oeis.org/A003309/list).
Reference implementations can be found at [Rosetta Code](https://rosettacode.org/wiki/Ludic_numbers).
# Scoring
This is code-golf. Shortest answer in every language wins.
#2: Post edited
by
Razetime
·
2021-09-21T04:28:58Z (about 3 years ago)
The Ludic Numbers
- The Ludic Numbers[FINALIZED]
- 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 `x`th number in `n`.- ```
- 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.
- The first 56 values can be seen here: [A003309](http://oeis.org/A003309/list).
- Reference implementations can be found at [Rosetta Code](https://rosettacode.org/wiki/Ludic_numbers).
- # Scoring
- This is code-golf. Shortest answer in every language wins.
- 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 `x`th 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](http://oeis.org/A003309/list).
- Reference implementations can be found at [Rosetta Code](https://rosettacode.org/wiki/Ludic_numbers).
- # Scoring
- This is code-golf. Shortest answer in every language wins.
#1: Initial revision
by
Razetime
·
2021-09-17T07:19:21Z (about 3 years ago)
The Ludic Numbers
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 `x`th number in `n`.
```
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.
The first 56 values can be seen here: [A003309](http://oeis.org/A003309/list).
Reference implementations can be found at [Rosetta Code](https://rosettacode.org/wiki/Ludic_numbers).
# Scoring
This is code-golf. Shortest answer in every language wins.