Ludic numbers   are related to prime numbers as they are generated by a sieve quite like the Sieve of Eratosthenes is used to generate prime numbers.

The first ludic number is   1.

To generate succeeding ludic numbers create an array of increasing integers starting from   2.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
(Loop)

 Take the first member of the resultant array as the next ludic number   2.
 Remove every   2nd   indexed item from the array (including the first).
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...
 (Unrolling a few loops...)
 Take the first member of the resultant array as the next ludic number   3.
 Remove every   3rd   indexed item from the array (including the first).
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 ...
 Take the first member of the resultant array as the next ludic number   5.
 Remove every   5th   indexed item from the array (including the first).
5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 ...
 Take the first member of the resultant array as the next ludic number   7.
 Remove every   7th   indexed item from the array (including the first).
7 11 13 17 23 25 29 31 37 41 43 47 53 55 59 61 67 71 73 77 83 85 89 91 97 ...
  ... 
 Take the first member of the current array as the next ludic number   L.
 Remove every   Lth   indexed item from the array (including the first).
  ... 


Task

 Generate and show here the first 25 ludic numbers.
 How many ludic numbers are there less than or equal to 1000?
 Show the 2000..2005th ludic numbers.


Stretch goal

Show all triplets of ludic numbers < 250.

 A triplet is any three numbers     



x
,


{\displaystyle x,}

   



x
+
2
,


{\displaystyle x+2,}

   



x
+
6


{\displaystyle x+6}

      where all three numbers are also ludic numbers. 


ludicGen: function [nmax][
    result: [1]
    lst: new 2..nmax+1
    i: 0
    worked: false
    while [and? [not? empty? lst] [i < size lst]][
        item: lst\[i]
        result: result ++ item
        del: 0
        worked: false
        while [del < size lst][
            worked: true
            remove 'lst .index del
            del: dec del + item
        ]
        if not? worked -> i: i + 1
    ]
    return result
]
 
ludics: ludicGen 25000
 
print "The first 25 ludic numbers:"
print first.n: 25 ludics
 
leThan1000: select ludics => [& =< 1000]
print ["\nThere are" size leThan1000 "ludic numbers less than/or equal to 1000\n"]
 
print ["The ludic numbers from 2000th to 2005th are:" slice ludics 1999 2004 "\n"]
 
print "The triplets of ludic numbers less than 250 are:"
print map select ludics 'x [
    all? @[ x < 250
            contains? ludics x+2
            contains? ludics x+6
    ]
] 't -> @[t, t+2, t+6]