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. 


/**
 * Boilerplate to simply get an array filled between 2 numbers
 * @param {!number} s Start here (inclusive)
 * @param {!number} e End here (inclusive)
 */
const makeArr = (s, e) => new Array(e + 1 - s).fill(s).map((e, i) => e + i);
 
/**
 * Remove every n-th element from the given array
 * @param {!Array} arr
 * @param {!number} n
 * @return {!Array}
 */
const filterAtInc = (arr, n) => arr.filter((e, i) => (i + 1) % n);
 
/**
 * Generate ludic numbers
 * @param {!Array} arr
 * @param {!Array} result
 * @return {!Array}
 */
const makeLudic = (arr, result) => {
  const iter = arr.shift();
  result.push(iter);
  return arr.length ? makeLudic(filterAtInc(arr, iter), result) : result;
};
 
/**
 * Our Ludic numbers. This is a bit of a cheat, as we already know beforehand
 * up to where our seed array needs to go in order to exactly get to the
 * 2005th Ludic number.
 * @type {!Array<!number>}
 */
const ludicResult = makeLudic(makeArr(2, 21512), [1]);
 
 
// Below is just logging out the results.
/**
 * Given a number, return a function that takes an array, and return the
 * count of all elements smaller than the given
 * @param {!number} n
 * @return {!Function}
 */
const smallerThanN = n => arr => {
  return arr.reduce((p,c) => {
    return c <= n ? p + 1 : p
  }, 0)
};
const smallerThan1K = smallerThanN(1000);
 
console.log('\nFirst 25 Ludic Numbers:');
console.log(ludicResult.filter((e, i) => i < 25).join(', '));
 
console.log('\nTotal Ludic numbers smaller than 1000:');
console.log(smallerThan1K(ludicResult));
 
console.log('\nThe 2000th to 2005th ludic numbers:');
console.log(ludicResult.filter((e, i) => i > 1998).join(', '));
 
console.log('\nTriplets smaller than 250:');
ludicResult.forEach(e => {
  if (e + 6 < 250 && ludicResult.indexOf(e + 2) > 0 && ludicResult.indexOf(e + 6) > 0) {
    console.log([e, e + 2, e + 6].join(', '));
  }
});