Ludic numbers

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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).

• ...