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 2’nd indexed item from the array (including the first).

234567891011121314151617181920212223242526...
 (Unrolling a few loops…)
 Take the first member of the resultant array as the next Ludic number 3.
 Remove every 3’rd indexed item from the array (including the first).

35 7911 131517 192123 252729 313335 373941 434547 4951...
 Take the first member of the resultant array as the next Ludic number 5.
 Remove every 5’th indexed item from the array (including the first).

57 11 13 171923 25 29 313537 41 43 474953 55 59 616567 71 73 77 ...
 Take the first member of the resultant array as the next Ludic number 7.
 Remove every 7’th indexed item from the array (including the first).

711 13 17 23 25 293137 41 43 47 53 555961 67 71 73 77 838589 91 97 ...
 …
 Take the first member of the current array as the next Ludic number L.
 Remove every L’th 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..2005’th ludic numbers.
 A triplet is any three numbers x, x + 2, x + 6 where all three numbers are also ludic numbers. Show all triplets of ludic numbers < 250 (Stretch goal)
#include <vector> #include <iostream> using namespace std; class ludic { public: void ludicList() { _list.push_back( 1 ); vector<int> v; for( int x = 2; x < 22000; x++ ) v.push_back( x ); while( true ) { vector<int>::iterator i = v.begin(); int z = *i; _list.push_back( z ); while( true ) { i = v.erase( i ); if( distance( i, v.end() ) <= z  1 ) break; advance( i, z  1 ); } if( v.size() < 1 ) return; } } void show( int s, int e ) { for( int x = s; x < e; x++ ) cout << _list[x] << " "; } void findTriplets( int e ) { int lu, x = 0; while( _list[x] < e ) { lu = _list[x]; if( inList( lu + 2 ) && inList( lu + 6 ) ) cout << "(" << lu << " " << lu + 2 << " " << lu + 6 << ")\n"; x++; } } int count( int e ) { int x = 0, c = 0; while( _list[x++] <= 1000 ) c++; return c; } private: bool inList( int lu ) { for( int x = 0; x < 250; x++ ) if( _list[x] == lu ) return true; return false; } vector<int> _list; }; int main( int argc, char* argv[] ) { ludic l; l.ludicList(); cout << "first 25 ludic numbers:" << "\n"; l.show( 0, 25 ); cout << "\n\nThere are " << l.count( 1000 ) << " ludic numbers <= 1000" << "\n"; cout << "\n2000 to 2005'th ludic numbers:" << "\n"; l.show( 1999, 2005 ); cout << "\n\nall triplets of ludic numbers < 250:" << "\n"; l.findTriplets( 250 ); cout << "\n\n"; return system( "pause" ); }
 Output:
first 25 ludic numbers: 1 2 3 5 7 11 13 17 23 25 29 37 41 43 47 53 61 67 71 77 83 89 91 97 107 There are 142 ludic numbers <= 1000 2000 to 2005'th ludic numbers: 21475 21481 21487 21493 21503 21511 all triplets of ludic numbers < 250: (1 3 7) (5 7 11) (11 13 17) (23 25 29) (41 43 47) (173 175 179) (221 223 227) (233 235 239)
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