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. 


 
# Project : Ludic numbers
 
ludic = list(300)
resludic = []
nr = 1
for n = 1 to len(ludic)
     ludic[n] = n+1
next
see "the first 25 Ludic numbers are:" + nl
ludicnumbers(ludic)
showarray(resludic)
see nl
 
see "Ludic numbers below 1000: " 
ludic = list(3000)
resludic = []
for n = 1 to len(ludic)
     ludic[n] = n+1
next
ludicnumbers(ludic)
showarray2(resludic)
see nr
see nl + nl
 
see "the 2000..2005th Ludic numbers are:" + nl
ludic = list(60000)
resludic = []
for n = 1 to len(ludic)
     ludic[n] = n+1
next
ludicnumbers(ludic)
showarray3(resludic)
 
func ludicnumbers(ludic)
      for n = 1 to len(ludic)
          delludic = [] 
          for m = 1 to len(ludic) step ludic[1]
              add(delludic, m)
          next
          add(resludic, ludic[1])
          for p = len(delludic)  to 1 step -1
              del(ludic, delludic[p])
          next
      next 
 
func showarray(vect)
      see "[1, "
      svect = ""
      for n = 1 to 24
          svect = svect + vect[n] + ", "
      next
      svect = left(svect, len(svect) - 2)
      see svect
      see "]" + nl
 
func showarray2(vect)
      for n = 1 to len(vect)
          if vect[n] <= 1000
             nr = nr + 1
          ok
      next
      return nr
 
func showarray3(vect)
      see "["
      svect = ""
      for n = 1999 to 2004
          svect = svect + vect[n] + ", "
      next
      svect = left(svect, len(svect) - 2)
      see svect
      see "]" + nl 
 